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In computational complexity theory, the Cook–Levin theorem, also known as Cook's theorem, states that the Boolean satisfiability problem is NP-complete. That is, any problem in NP can be reduced in polynomial time by a deterministic Turing machine to the problem of determining whether a Boolean formula is satisfiable.

The theorem is named after Stephen Cook and Leonid Levin.

An important consequence of the theorem is that if there exists a deterministic polynomial time algorithm for solving Boolean satisfiability, then there exists a deterministic polynomial time algorithm for solving all problems in NP. Crucially, the same follows for any NP complete problem.

The question of whether such an algorithm exists is called the P versus NP problem and it is widely considered the most important unsolved problem in theoretical computer science.

Contributions

The concept of NP-completeness was developed in the late 1960s and early 1970s in parallel by researchers in the US and the USSR. In the US in 1971, Stephen Cook published his paper "The complexity of theorem proving procedures"^[1] in conference proceedings of the newly founded ACM Symposium on Theory of Computing. Richard Karp's subsequent paper, "Reducibility among combinatorial problems",^[2] generated renewed interest in Cook's paper by providing a list of 21 NP-complete problems. Cook and Karp received a Turing Award for this work.

The theoretical interest in NP-completeness was also enhanced by the work of Theodore P. Baker, John Gill, and Robert Solovay who showed that solving NP-problems in Oracle machine models requires exponential time. That is, there exists an oracle A such that, for all subexponential deterministic time complexity classes T, the relativized complexity class NP^A is not a subset of T^A. In particular, for this oracle, P^A ≠ NP^A.^[3]

In the USSR, a result equivalent to Baker, Gill, and Solovay's was published in 1969 by M. Dekhtiar.^[4] Later Levin's paper, "Universal search problems",^[5] was published in 1973, although it was mentioned in talks and submitted for publication a few years earlier.

Levin's approach was slightly different from Cook's and Karp's in that he considered search problems, which require finding solutions rather than simply determining existence. He provided 6 such NP-complete search problems, or universal problems, and additionally found that each has an algorithm which solves it in optimal time.Template:Vague

Definitions

A decision problem is in NP if it can be solved by a non-deterministic algorithm in polynomial time.

An instance of the Boolean satisfiability problem is a Boolean expression that combines Boolean variables using Boolean operators.

An expression is satisfiable if there is some assignment of truth values to the variables that makes the entire expression true.

Idea

Given any decision problem in NP, construct a non-deterministic machine that solves it in polynomial time. Then for each input to that machine, build a Boolean expression which says that the input is passed to the machine, the machine runs correctly, and the machine halts and answers "yes". Then the expression can be satisfied if and only if there is a way for the machine to run correctly and answer "yes", so the satisfiability of the constructed expression is equivalent to asking whether or not the machine will answer "yes".

Proof

This proof is based on the one given by Garey and Johnson.^[6]

There are two parts to proving that the Boolean satisfiability problem (SAT) is NP-complete. One is to show that SAT is an NP problem. The other is to show that every NP problem can be reduced to an instance of a SAT problem by a polynomial-time many-one reduction.

SAT is in NP because any assignment of Boolean values to Boolean variables that is claimed to satisfy the given expression can be verified in polynomial time by a deterministic Turing machine. (The statements verifiable in polynomial time by a deterministic Turing machine and solvable in polynomial time by a non-deterministic Turing machine are totally equivalent, and the proof can be found in many textbooks, for example Sipser's Introduction to the Theory of Computation, section 7.3.).

Now suppose that a given problem in NP can be solved by the nondeterministic Turing machine M = (Q, Σ, s, F, δ), where Q is the set of states, Σ is the alphabet of tape symbols, s ∈ Q is the initial state, F ⊆ Q is the set of accepting states, and δ ⊆ ((Q \ F) × Σ) × (Q × Σ × {−1, +1}) is the transition relation. Suppose further that M accepts or rejects an instance of the problem in time p(n) where n is the size of the instance and p is a polynomial function.

For each input, I, we specify a Boolean expression which is satisfiable if and only if the machine M accepts I.

The Boolean expression uses the variables set out in the following table. Here, q ∈ Q, −p(n) ≤ i ≤ p(n), j ∈ Σ, and 0 ≤ k ≤ p(n).

Variables	Intended interpretation	How many?
T_ijk	True if tape cell i contains symbol j at step k of the computation.	O(p(n)²)
H_ik	True if the M's read/write head is at tape cell i at step k of the computation.	O(p(n)²)
Q_qk	True if M is in state q at step k of the computation.	O(p(n))

Define the Boolean expression B to be the conjunction of the sub-expressions in the following table, for all −p(n) ≤ i ≤ p(n) and 0 ≤ k ≤ p(n):

Expression	Conditions	Interpretation	How many?
T_ij0	Tape cell i initially contains symbol j	Initial contents of the tape. For i > n-1 and i < 0, outside of the actual input I, the initial symbol is the special default/blank symbol.	O(p(n))
Q_s0		Initial state of M.	1
H₀₀		Initial position of read/write head.	1
T_ijk → ¬ T_ij′k	j ≠ j′	One symbol per tape cell.	O(p(n)²)
T_ijk ∧ T_ij′(k+1) → H_ik	j ≠ j′	Tape remains unchanged unless written.	O(p(n)²)
Q_qk → ¬ Q_q′k	q ≠ q′	Only one state at a time.	O(p(n))
H_ik → ¬ H_i′k	i ≠ i′	Only one head position at a time.	O(p(n)³)
(H_ik ∧ Q_qk ∧ T_iσk) → $\bigvee$ _{(q, σ, q′, σ′, d) ∈ δ}(H_(i+d)(k+1) ∧ Q_q′(k+1) ∧ T_iσ′(k+1))	k<p(n)	Possible transitions at computation step k when head is at position i.	O(p(n)²)
$\bigvee$ _{f ∈ F} Q_fp(n)		Must finish in an accepting state.	1

If there is an accepting computation for M on input I, then B is satisfiable by assigning T_ijk, H_ik and Q_ik their intended interpretations. On the other hand, if B is satisfiable, then there is an accepting computation for M on input I that follows the steps indicated by the assignments to the variables.

There are O(p(n)²) Boolean variables, each encodeable in space O(log p(n)). The number of clauses is O(p(n)³) so the size of B is O(log(p(n))p(n)³). Thus the transformation is certainly a polynomial-time many-one reduction, as required.

Consequences

The proof shows that any problem in NP can be reduced in polynomial time (in fact, logarithmic space suffices) to an instance of the Boolean satisfiability problem. This means that if the Boolean satisfiability problem could be solved in polynomial time by a deterministic Turing machine, then all problems in NP could be solved in polynomial time, and so the complexity class NP would be equal to the complexity class P.

The significance of NP-completeness was made clear by the publication in 1972 of Richard Karp's landmark paper, "Reducibility among combinatorial problems", in which he showed that 21 diverse combinatorial and graph theoretical problems, each infamous for its intractability, are NP-complete.^[2]

Karp showed each of his problems to be NP-complete by reducing another problem (already shown to be NP-complete) to that problem. For example, he showed the problem 3SAT (the Boolean satisfiability problem for expressions in conjunctive normal form with exactly three variables or negations of variables per clause) to be NP-complete by showing how to reduce (in polynomial time) any instance of SAT to an equivalent instance of 3SAT. (First you modify the proof of the Cook–Levin theorem, so that the resulting formula is in conjunctive normal form, then you introduce new variables to split clauses with more than 3 atoms. For example, the clause (A ∨ B ∨ C ∨ D) can be replaced by the conjunction of clauses (A ∨ B ∨ Z) ∧ (¬Z ∨ C ∨ D), where Z is a new variable which will not be used anywhere else in the expression. Clauses with fewer than 3 atoms can be padded; for example, A can be replaced by (A ∨ A ∨ A), and (A ∨ B) can be replaced by (A ∨ B ∨ B) ).

Garey and Johnson presented more than 300 NP-complete problems in their book Computers and Intractability: A Guide to the Theory of NP-Completeness,^[6] and new problems are still being discovered to be within that complexity class.

Although many practical instances of SAT can be solved by heuristic methods, the question of whether there is a deterministic polynomial-time algorithm for SAT (and consequently all other NP-complete problems) is still a famous unsolved problem, despite decades of intense effort by complexity theorists, mathematical logicians, and others. For more details, see the article P=NP problem.

References

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↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang Not perhaps one of the best-identified of Singapore points of interest, the Spice Garden at Fort Canning Park is a veritable trove of Singapore's natural historical past, with over 100 varieties of vegetation and trees lining its trails.

There isn't a double taxation here. Property tax is imposed based mostly on property possession. It is totally different from revenue tax on the rental income, which is a tax on the income which an individual earns. It's free, and you will automatically receive property market updates, the most recent actual property developments, new guidelines and insurance policies, and lots of extra. Find out more On the similar time, monetary institutions have been lengthening the tenures of residential property loans. Over the past three years, the typical tenure for brand spanking new residential property loans has increased from 25 to 29 years. Greater than 45% of new residential property loans granted by financial establishments have tenures exceeding 30 years. Pasir Ris, Simei, Tampines Lease Property District 19 Related Articles

Mr Tharman Shanmugaratnam, Chairman of MAS, said, "Monetary conditions worldwide are removed from normal. QE3 and low rates of interest have made credit simple, but this may finally change. We're taking this step now to require extra prudent lending, and will continue to observe the property market rigorously. We will do what it takes to cool the market, and keep away from a bubble that will ultimately harm borrowers and destabilise our financial system." Rising office sector leads real property market performance, while prime retail and business park segments reasonable and residential sector continues in decline Opportunity to amass a row of 3 adjoining store houses within Little India Conservation Space D10) Holland / Tanglin HDB Frequent Room with Aircon

b. A property held by 2 or extra persons as tenants in frequent means that each proprietor has a specified or distinct share or proportion in the property. For instance, such share might be on an equal basis (50%-50%) or 90% - 10% basis and so on. Each owner might be able to dispose his share within the property both by sale or under his Will. Upon the dying of 1 proprietor, the surviving co-owner(s) do(es) not take over the deceased's curiosity in the property as is in the case of joint tenancy. His share shall be handed below his will or in accordance with the regulation of intestacy, because the case may be.

In the meantime, inside design duties went to the group at Design Intervention. Unsurprisingly, Chan's impressive home garnered the 11th Singapore Institute of Architecture Design Award this year. "The Jury is impressed with the result of what was a really shut collaboration between architect and proprietor, which turned out to be a really up-to-date tackle a tropical language of structure." explains the judging panel along with their verdict. HONG LEONG HOLDINGS LIMITED (HLH) was established in 1968 as the group's privately held property funding and property holding car. It has developed about 40 residential properties thus far and markets/manages 12 industrial initiatives. KF Property Network Pte Ltd any condo inside a constructing; a) An condo in a building

Rates of interest are extraordinarily low, globally and in Singapore, and continue to add fuel to our property market. We've to take this additional spherical of measures now, to examine current market tendencies and keep away from a extra serious correction in costs further down the road,ђ mentioned Deputy Prime Minister and Minister for Finance Tharman Shanmugaratnam. See your Banker to have an evaluation of your monetary state of affairs. Decide on the range of Property you might be keen to speculate. Verify for the best rate on the town or contact our accomplice bankers for help if required. >> Step 2 Resolve your wants and make your want list The lawyer's fees do not include stamp fees or disbursements properly incurred bythe lawyer. Promoting Your House or Flat 2xxxpsf view this challenge

Under the brand new property tax construction, properties with AV under $eight,000 will enjoy zero property tax. apartment in singapore reality, all homes with AVs as much as $59,000 will both pay no property tax or lower efficient property tax, as compared to the property tax payable beneath the earlier construction. The new rates shall be phased over in over two years, with the modifications taking impact on 1 January 2014 and 1 January 2015. We've got thus stored property tax as our wealth tax primarily based on property possession. Deborah Regulation from Expat Realtor shares her property market replace, plus top rental flats and houses at present out there to lease for a borrower with no excellent residential property loan. Hire Property District 14 Lease Property District 15 Rent Property District sixteen PropNex Property TV
↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang (pdf) Not perhaps one of the best-identified of Singapore points of interest, the Spice Garden at Fort Canning Park is a veritable trove of Singapore's natural historical past, with over 100 varieties of vegetation and trees lining its trails.

There isn't a double taxation here. Property tax is imposed based mostly on property possession. It is totally different from revenue tax on the rental income, which is a tax on the income which an individual earns. It's free, and you will automatically receive property market updates, the most recent actual property developments, new guidelines and insurance policies, and lots of extra. Find out more On the similar time, monetary institutions have been lengthening the tenures of residential property loans. Over the past three years, the typical tenure for brand spanking new residential property loans has increased from 25 to 29 years. Greater than 45% of new residential property loans granted by financial establishments have tenures exceeding 30 years. Pasir Ris, Simei, Tampines Lease Property District 19 Related Articles

Mr Tharman Shanmugaratnam, Chairman of MAS, said, "Monetary conditions worldwide are removed from normal. QE3 and low rates of interest have made credit simple, but this may finally change. We're taking this step now to require extra prudent lending, and will continue to observe the property market rigorously. We will do what it takes to cool the market, and keep away from a bubble that will ultimately harm borrowers and destabilise our financial system." Rising office sector leads real property market performance, while prime retail and business park segments reasonable and residential sector continues in decline Opportunity to amass a row of 3 adjoining store houses within Little India Conservation Space D10) Holland / Tanglin HDB Frequent Room with Aircon

b. A property held by 2 or extra persons as tenants in frequent means that each proprietor has a specified or distinct share or proportion in the property. For instance, such share might be on an equal basis (50%-50%) or 90% - 10% basis and so on. Each owner might be able to dispose his share within the property both by sale or under his Will. Upon the dying of 1 proprietor, the surviving co-owner(s) do(es) not take over the deceased's curiosity in the property as is in the case of joint tenancy. His share shall be handed below his will or in accordance with the regulation of intestacy, because the case may be.

In the meantime, inside design duties went to the group at Design Intervention. Unsurprisingly, Chan's impressive home garnered the 11th Singapore Institute of Architecture Design Award this year. "The Jury is impressed with the result of what was a really shut collaboration between architect and proprietor, which turned out to be a really up-to-date tackle a tropical language of structure." explains the judging panel along with their verdict. HONG LEONG HOLDINGS LIMITED (HLH) was established in 1968 as the group's privately held property funding and property holding car. It has developed about 40 residential properties thus far and markets/manages 12 industrial initiatives. KF Property Network Pte Ltd any condo inside a constructing; a) An condo in a building

Rates of interest are extraordinarily low, globally and in Singapore, and continue to add fuel to our property market. We've to take this additional spherical of measures now, to examine current market tendencies and keep away from a extra serious correction in costs further down the road,ђ mentioned Deputy Prime Minister and Minister for Finance Tharman Shanmugaratnam. See your Banker to have an evaluation of your monetary state of affairs. Decide on the range of Property you might be keen to speculate. Verify for the best rate on the town or contact our accomplice bankers for help if required. >> Step 2 Resolve your wants and make your want list The lawyer's fees do not include stamp fees or disbursements properly incurred bythe lawyer. Promoting Your House or Flat 2xxxpsf view this challenge

Under the brand new property tax construction, properties with AV under $eight,000 will enjoy zero property tax. apartment in singapore reality, all homes with AVs as much as $59,000 will both pay no property tax or lower efficient property tax, as compared to the property tax payable beneath the earlier construction. The new rates shall be phased over in over two years, with the modifications taking impact on 1 January 2014 and 1 January 2015. We've got thus stored property tax as our wealth tax primarily based on property possession. Deborah Regulation from Expat Realtor shares her property market replace, plus top rental flats and houses at present out there to lease for a borrower with no excellent residential property loan. Hire Property District 14 Lease Property District 15 Rent Property District sixteen PropNex Property TV, translated into English by One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
↑ ^6.0 ^6.1 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

[1] 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

[Karp-2] 2.0 ^2.1 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

[3] One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

[4] One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang Not perhaps one of the best-identified of Singapore points of interest, the Spice Garden at Fort Canning Park is a veritable trove of Singapore's natural historical past, with over 100 varieties of vegetation and trees lining its trails.

There isn't a double taxation here. Property tax is imposed based mostly on property possession. It is totally different from revenue tax on the rental income, which is a tax on the income which an individual earns. It's free, and you will automatically receive property market updates, the most recent actual property developments, new guidelines and insurance policies, and lots of extra. Find out more On the similar time, monetary institutions have been lengthening the tenures of residential property loans. Over the past three years, the typical tenure for brand spanking new residential property loans has increased from 25 to 29 years. Greater than 45% of new residential property loans granted by financial establishments have tenures exceeding 30 years. Pasir Ris, Simei, Tampines Lease Property District 19 Related Articles

Mr Tharman Shanmugaratnam, Chairman of MAS, said, "Monetary conditions worldwide are removed from normal. QE3 and low rates of interest have made credit simple, but this may finally change. We're taking this step now to require extra prudent lending, and will continue to observe the property market rigorously. We will do what it takes to cool the market, and keep away from a bubble that will ultimately harm borrowers and destabilise our financial system." Rising office sector leads real property market performance, while prime retail and business park segments reasonable and residential sector continues in decline Opportunity to amass a row of 3 adjoining store houses within Little India Conservation Space D10) Holland / Tanglin HDB Frequent Room with Aircon

b. A property held by 2 or extra persons as tenants in frequent means that each proprietor has a specified or distinct share or proportion in the property. For instance, such share might be on an equal basis (50%-50%) or 90% - 10% basis and so on. Each owner might be able to dispose his share within the property both by sale or under his Will. Upon the dying of 1 proprietor, the surviving co-owner(s) do(es) not take over the deceased's curiosity in the property as is in the case of joint tenancy. His share shall be handed below his will or in accordance with the regulation of intestacy, because the case may be.

In the meantime, inside design duties went to the group at Design Intervention. Unsurprisingly, Chan's impressive home garnered the 11th Singapore Institute of Architecture Design Award this year. "The Jury is impressed with the result of what was a really shut collaboration between architect and proprietor, which turned out to be a really up-to-date tackle a tropical language of structure." explains the judging panel along with their verdict. HONG LEONG HOLDINGS LIMITED (HLH) was established in 1968 as the group's privately held property funding and property holding car. It has developed about 40 residential properties thus far and markets/manages 12 industrial initiatives. KF Property Network Pte Ltd any condo inside a constructing; a) An condo in a building

Rates of interest are extraordinarily low, globally and in Singapore, and continue to add fuel to our property market. We've to take this additional spherical of measures now, to examine current market tendencies and keep away from a extra serious correction in costs further down the road,ђ mentioned Deputy Prime Minister and Minister for Finance Tharman Shanmugaratnam. See your Banker to have an evaluation of your monetary state of affairs. Decide on the range of Property you might be keen to speculate. Verify for the best rate on the town or contact our accomplice bankers for help if required. >> Step 2 Resolve your wants and make your want list The lawyer's fees do not include stamp fees or disbursements properly incurred bythe lawyer. Promoting Your House or Flat 2xxxpsf view this challenge

Under the brand new property tax construction, properties with AV under $eight,000 will enjoy zero property tax. apartment in singapore reality, all homes with AVs as much as $59,000 will both pay no property tax or lower efficient property tax, as compared to the property tax payable beneath the earlier construction. The new rates shall be phased over in over two years, with the modifications taking impact on 1 January 2014 and 1 January 2015. We've got thus stored property tax as our wealth tax primarily based on property possession. Deborah Regulation from Expat Realtor shares her property market replace, plus top rental flats and houses at present out there to lease for a borrower with no excellent residential property loan. Hire Property District 14 Lease Property District 15 Rent Property District sixteen PropNex Property TV

[5] One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang (pdf) Not perhaps one of the best-identified of Singapore points of interest, the Spice Garden at Fort Canning Park is a veritable trove of Singapore's natural historical past, with over 100 varieties of vegetation and trees lining its trails.

There isn't a double taxation here. Property tax is imposed based mostly on property possession. It is totally different from revenue tax on the rental income, which is a tax on the income which an individual earns. It's free, and you will automatically receive property market updates, the most recent actual property developments, new guidelines and insurance policies, and lots of extra. Find out more On the similar time, monetary institutions have been lengthening the tenures of residential property loans. Over the past three years, the typical tenure for brand spanking new residential property loans has increased from 25 to 29 years. Greater than 45% of new residential property loans granted by financial establishments have tenures exceeding 30 years. Pasir Ris, Simei, Tampines Lease Property District 19 Related Articles

Mr Tharman Shanmugaratnam, Chairman of MAS, said, "Monetary conditions worldwide are removed from normal. QE3 and low rates of interest have made credit simple, but this may finally change. We're taking this step now to require extra prudent lending, and will continue to observe the property market rigorously. We will do what it takes to cool the market, and keep away from a bubble that will ultimately harm borrowers and destabilise our financial system." Rising office sector leads real property market performance, while prime retail and business park segments reasonable and residential sector continues in decline Opportunity to amass a row of 3 adjoining store houses within Little India Conservation Space D10) Holland / Tanglin HDB Frequent Room with Aircon

b. A property held by 2 or extra persons as tenants in frequent means that each proprietor has a specified or distinct share or proportion in the property. For instance, such share might be on an equal basis (50%-50%) or 90% - 10% basis and so on. Each owner might be able to dispose his share within the property both by sale or under his Will. Upon the dying of 1 proprietor, the surviving co-owner(s) do(es) not take over the deceased's curiosity in the property as is in the case of joint tenancy. His share shall be handed below his will or in accordance with the regulation of intestacy, because the case may be.

In the meantime, inside design duties went to the group at Design Intervention. Unsurprisingly, Chan's impressive home garnered the 11th Singapore Institute of Architecture Design Award this year. "The Jury is impressed with the result of what was a really shut collaboration between architect and proprietor, which turned out to be a really up-to-date tackle a tropical language of structure." explains the judging panel along with their verdict. HONG LEONG HOLDINGS LIMITED (HLH) was established in 1968 as the group's privately held property funding and property holding car. It has developed about 40 residential properties thus far and markets/manages 12 industrial initiatives. KF Property Network Pte Ltd any condo inside a constructing; a) An condo in a building

Rates of interest are extraordinarily low, globally and in Singapore, and continue to add fuel to our property market. We've to take this additional spherical of measures now, to examine current market tendencies and keep away from a extra serious correction in costs further down the road,ђ mentioned Deputy Prime Minister and Minister for Finance Tharman Shanmugaratnam. See your Banker to have an evaluation of your monetary state of affairs. Decide on the range of Property you might be keen to speculate. Verify for the best rate on the town or contact our accomplice bankers for help if required. >> Step 2 Resolve your wants and make your want list The lawyer's fees do not include stamp fees or disbursements properly incurred bythe lawyer. Promoting Your House or Flat 2xxxpsf view this challenge

Under the brand new property tax construction, properties with AV under $eight,000 will enjoy zero property tax. apartment in singapore reality, all homes with AVs as much as $59,000 will both pay no property tax or lower efficient property tax, as compared to the property tax payable beneath the earlier construction. The new rates shall be phased over in over two years, with the modifications taking impact on 1 January 2014 and 1 January 2015. We've got thus stored property tax as our wealth tax primarily based on property possession. Deborah Regulation from Expat Realtor shares her property market replace, plus top rental flats and houses at present out there to lease for a borrower with no excellent residential property loan. Hire Property District 14 Lease Property District 15 Rent Property District sixteen PropNex Property TV, translated into English by One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

[Garey-6] 6.0 ^6.1 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

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-"Why does my computer keep freezing up?" I was asked by a lot of persons the cause of their pc freeze issues. And I am fed up with spending much time inside answering the query time plus time again. This post is to tell we the real cause of your PC Freezes.<br><br>Firstly, you need to use the Antivirus or safety tool plus run a scan on your computer. It is possible which a computer is infected with virus or malware that slows down your computer. If there is nothing found in the scanning report, it will be the RAM which cause the issue.<br><br>So what should you look for whenever you compare registry products. Many of the registry products accessible now, have rather similar features. The principal ones which you need to be trying to find are these.<br><br>In order to remove the programs on a computer, Windows Installer should be in a healthy state. If its installation is corrupted we could get error 1721 in Windows 7, Vista and XP during the system removal task. Just re-registering its component files would resolve the issue.<br><br>Besides, should you will get a [http://bestregistrycleanerfix.com/tune-up-utilities tuneup utilities 2014] which may do the job for you effectively plus rapidly, then why not? There is 1 such system, RegCure that is especially good and complete. It has features that additional cleaners never have. It is the most recommended registry cleaner today.<br><br>2)Fix the Windows registry to accelerate PC- The registry is a complex section of your computer which holds different types of data within the things you do on the computer each day. Coincidentally, over time the registry might become cluttered with information and/or will obtain some kind of virus. This is truly important plus you MUST receive this problem fixed right away, otherwise we run the risk of your computer being permanently damage and/or the sensitive info (passwords, etc.) can be stolen.<br><br>It is important that we remove obsolete registry entries from a program on a regular basis, in the event you want your system to run faster, that is. If you don't keep a registry clean, a time comes when the program usually stop functioning altogether. Next, a only way would be to reformat the hard drive and begin over!<br><br>Next, there is an effortless method to deal with this issue. You are able to install a registry cleaner that there are it found on the internet. This software can help we find out these errors in a computer and clean them. It furthermore could figure out these malware plus other threats which influence the speed of the computer. So this software will speed up PC easier. You can choose one of these techniques to accelerate we computer.
+In [[computational complexity theory]], the '''Cook–Levin theorem''', also known as '''Cook's theorem''', states that the [[Boolean satisfiability problem]] is [[NP-completeness|NP-complete]].  That is, any problem in [[NP (complexity)|NP]] can be [[reduction (complexity)|reduced]] in polynomial time by a [[deterministic Turing machine]] to the problem of determining whether a Boolean formula is satisfiable.
+The theorem is named after [[Stephen Cook]] and [[Leonid Levin]].
+An important consequence of the theorem is that if there exists a deterministic polynomial time algorithm for solving Boolean satisfiability, then there exists a deterministic polynomial time algorithm for solving ''all'' problems in [[NP (complexity)|NP]].  Crucially, the same follows for any [[NP complete]] problem.
+The question of whether such an algorithm exists is called the [[P versus NP problem]] and it is widely considered the most important unsolved problem in theoretical computer science.
+==Contributions==
+The concept of NP-completeness was developed in the late 1960s and early 1970s in parallel by researchers in the US and the [[USSR]].
+In the US in 1971, [[Stephen Cook]] published his paper "The complexity of theorem proving procedures"<ref>{{cite book|last=Cook|first=Stephen|authorlink=Stephen Cook|year=1971|chapter=The complexity of theorem proving procedures|chapterurl=http://portal.acm.org/citation.cfm?coll=GUIDE&dl=GUIDE&id=805047|title=Proceedings of the Third Annual ACM Symposium on Theory of Computing|pages=151–158}}</ref> in conference proceedings of the newly founded ACM [[Symposium on Theory of Computing]]. [[Richard Karp]]'s subsequent paper, "Reducibility among
+combinatorial problems",<ref name="Karp"/> generated renewed interest in Cook's paper by providing a [[Karp's 21 NP-complete problems|list of 21 NP-complete problems]]. Cook and Karp received a [[Turing Award]] for this work.
+<!--
+THIS IS POORLY WORDED:
+Another important contribution of Karp was to notice
+that many NP-complete problems, while seemingly intractable in the
+worst case, are actually easy for almost all random instances.{{Citation needed|date=March 2008}} In 1984, Levin
+extended this result by proving that some NP problems
+are complete in the average case as well.<ref>http://www.claymath.org/millennium/P_vs_NP/pvsnp.pdf</ref>
+-->
+The theoretical interest in NP-completeness was also enhanced by the work of Theodore P. Baker, John Gill, and [[Robert Solovay]] who showed that solving NP-problems in [[Oracle machine]] models requires exponential time. That is, there exists an oracle ''A'' such that, for all subexponential deterministic time complexity classes T, the relativized complexity class NP<sup>''A''</sup> is not a subset of T<sup>''A''</sup>. In particular, for this oracle, P<sup>''A''</sup>&nbsp;≠&nbsp;NP<sup>''A''</sup>.<ref>{{cite journal|author = T. P. Baker|coauthors = J. Gill, R. Solovay|title = Relativizations of the P = NP question|journal = SIAM Journal on Computing |volume = 4|issue = 4|pages = 431–442|year = 1975|doi = 10.1137/0204037}}</ref>
+In the USSR, a result equivalent to Baker, Gill, and Solovay's was published in 1969 by M. Dekhtiar.<ref>{{cite journal|last=Dekhtiar|first=M.|title = On the impossibility of eliminating exhaustive search in computing a function relative to its graph|journal = [[Proceedings of the USSR Academy of Sciences]]|volume = 14|pages = 1146–1148|year = 1969}} {{ru icon}}</ref> Later [[Leonid Levin|Levin]]'s paper, "Universal search problems",<ref>{{cite journal|last=Levin|first=Leonid|authorlink=Leonid Levin|title = Universal search problems ({{lang-ru|Универсальные задачи перебора}}, Universal'nye perebornye zadachi)|journal = Problems of Information Transmission ({{lang-ru|Проблемы передачи информации}}, Problemy Peredachi Informatsii)|volume = 9|issue = 3|pages = 115–116|year = 1973}} [http://www.mathnet.ru/php/getFT.phtml?jrnid=ppi&paperid=914&volume=9&year=1973&issue=3&fpage=115&what=fullt&option_lang=eng (pdf)] {{ru icon}}, translated into English by {{cite journal|last=Trakhtenbrot|first=B. A.|title = A survey of Russian approaches to ''perebor'' (brute-force searches) algorithms|journal = Annals of the History of Computing |volume = 6|issue = 4|pages = 384–400|year = 1984|doi=10.1109/MAHC.1984.10036}}</ref> was published in 1973, although it was mentioned in talks and submitted for publication a few years earlier.
+Levin's approach was slightly different from Cook's and Karp's in that he considered [[search problem]]s, which require finding solutions rather than simply determining existence. He provided 6 such NP-complete search problems, or ''universal problems'', and
+additionally found that each has an algorithm which solves it in optimal time.{{Vague|date=March 2008}}
+==Definitions==
+A [[decision problem]] is ''in [[NP (complexity)|NP]]'' if it can be solved by a [[non-deterministic algorithm]] in [[polynomial time]].
+An ''instance of the Boolean satisfiability problem'' is a [[Boolean expression]] that combines [[Boolean variable]]s using [[Logical connective|Boolean operator]]s.
+An expression is ''satisfiable'' if there is some assignment of [[truth value]]s to the variables that makes the entire expression true.
+==Idea==
+Given any decision problem in NP, construct a non-deterministic machine that solves it in polynomial time. Then for each input to that machine, build a Boolean expression which says that the input is passed to the machine, the machine runs correctly, and the machine halts and answers "yes". Then the expression can be satisfied if and only if there is a way for the machine to run correctly and answer "yes", so the satisfiability of the constructed expression is equivalent to asking whether or not the machine will answer "yes".
+==Proof==
+''This proof is based on the one given by Garey and Johnson.''<ref name="Garey">{{cite book|last=Garey|first=Michael R.|coauthors=David S. Johnson|title = Computers and Intractability: A Guide to the Theory of NP-Completeness|publisher = W. H. Freeman|year = 1979|isbn=0-7167-1045-5}}</ref>
+There are two parts to proving that the Boolean satisfiability problem (SAT) is NP-complete. One is to show that SAT is an NP problem. The other is to show that every NP problem can be reduced to an instance of a SAT problem by a [[polynomial-time many-one reduction]].
+SAT is in NP because any assignment of Boolean values to Boolean variables that is claimed to satisfy the given expression can be ''verified'' in polynomial time by a deterministic Turing machine. (The statements '''''verifiable''' in polynomial time by a '''deterministic''' Turing machine'' and '''''solvable''' in polynomial time by a '''non-deterministic''' Turing machine'' are totally equivalent, and the proof can be found in many textbooks, for example Sipser's ''Introduction to the Theory of Computation'', section 7.3.).
+Now suppose that a given problem in NP can be solved by the [[nondeterministic Turing machine]] ''M''&nbsp;=&nbsp;(''Q'',&nbsp;Σ,&nbsp;''s'',&nbsp;''F'',&nbsp;δ), where ''Q'' is the set of states, Σ is the alphabet of tape symbols, ''s''&nbsp;∈&nbsp;''Q'' is the initial state, ''F''&nbsp;⊆&nbsp;''Q'' is the set of accepting states, and δ&nbsp;⊆&nbsp;((''Q''&nbsp;\&nbsp;''F'')&nbsp;×&nbsp;Σ)&nbsp;×&nbsp;(''Q''&nbsp;×&nbsp;Σ&nbsp;×&nbsp;{−1,&nbsp;+1}) is the transition relation. Suppose further that ''M'' accepts or rejects an instance of the problem in time ''p''(''n'') where ''n'' is the size of the instance and ''p'' is a polynomial function.
+For each input, ''I'', we specify a Boolean expression which is satisfiable [[if and only if]] the machine ''M'' accepts ''I''.
+The Boolean expression uses the variables set out in the following table. Here, ''q''&nbsp;∈&nbsp;''Q'', −''p''(''n'')&nbsp;≤&nbsp;''i''&nbsp;≤&nbsp;''p''(''n''), ''j''&nbsp;∈&nbsp;Σ, and 0&nbsp;≤&nbsp;''k''&nbsp;≤&nbsp;''p''(''n'').
+{| class="wikitable"
+!Variables
+!Intended interpretation
+!How many?
+|-
+|''T<sub>ijk</sub>''
+|True if tape cell ''i'' contains symbol ''j'' at step ''k'' of the computation.
+|O(''p''(''n'')<sup>2</sup>)
+|-
+|''H<sub>ik</sub>''
+|True if the ''M''&#39;s read/write head is at tape cell ''i'' at step ''k'' of the computation.
+|O(''p''(''n'')<sup>2</sup>)
+|-
+|''Q<sub>qk</sub>''
+|True if ''M'' is in state ''q'' at step ''k'' of the computation.
+|O(''p''(''n''))
+|}
+Define the Boolean expression ''B'' to be the [[Logical conjunction|conjunction]] of the sub-expressions in the following table, for all −''p''(''n'')&nbsp;≤&nbsp;''i''&nbsp;≤&nbsp;''p''(''n'') and 0&nbsp;≤&nbsp;''k''&nbsp;≤&nbsp;''p''(''n''):
+{| class="wikitable"
+!Expression
+!Conditions
+!Interpretation
+!How many?
+|-
+|''T<sub>ij0</sub>''
+|Tape cell ''i'' initially contains symbol ''j''
+|Initial contents of the tape.  For ''i'' > ''n''-1 and ''i'' < 0, outside of the actual input ''I'', the initial symbol is the special default/blank symbol.
+|O(''p''(''n''))
+|-
+|''Q<sub>s0</sub>''
+|&nbsp;
+|Initial  state of ''M''.
+|1
+|-
+|''H<sub>00</sub>''
+|&nbsp;
+|Initial position of read/write head.
+|1
+|-
+|''T<sub>ijk</sub>'' → ¬ ''T<sub>ij&prime;k</sub>''
+|''j'' ≠ ''j&prime;''
+|One symbol per tape cell.
+|O(''p''(''n'')<sup>2</sup>)
+|-
+|''T<sub>ijk</sub>'' ∧ ''T''<sub>''ij&prime;''(''k''+1)</sub> → ''H<sub>ik</sub>''
+|''j'' ≠ ''j&prime;''
+|Tape remains unchanged unless written.
+|O(''p''(''n'')<sup>2</sup>)
+|-
+|''Q<sub>qk</sub>'' → ¬ ''Q<sub>q&prime;k</sub>''
+|''q'' ≠ ''q&prime;''
+|Only one state at a time.
+|O(''p''(''n''))
+|-
+|''H<sub>ik</sub>'' → ¬ ''H<sub>i&prime;k</sub>''
+|''i'' ≠ ''i&prime;''
+|Only one head position at a time.
+|O(''p''(''n'')<sup>3</sup>)
+|-
+|(''H<sub>ik</sub>'' ∧ ''Q<sub>qk</sub>'' ∧ ''T<sub>iσk</sub>'') → <br><math>\bigvee</math><sub>(''q'', ''σ'', ''q&prime;'', ''σ&prime;'', ''d'') ∈ ''δ''</sub>(''H''<sub>(''i''+''d'')(''k''+1)</sub> ∧ ''Q''<sub>''q&prime;''(''k''+1)</sub> ∧ ''T''<sub>''iσ&prime;''(''k''+1)</sub>)
+|''k''<''p''(''n'')
+|Possible transitions at computation step ''k'' when head is at position ''i''.
+|O(''p''(''n'')<sup>2</sup>)
+|-
+|<math>\bigvee</math><sub>''f'' ∈ ''F''</sub> ''Q''<sub>''fp''(''n'')</sub>
+|
+|Must finish in an accepting state.
+|1
+|}
+If there is an accepting computation for ''M'' on input ''I'', then ''B'' is satisfiable by assigning ''T''<sub>''ijk''</sub>, ''H''<sub>''ik''</sub> and ''Q''<sub>''ik''</sub> their intended interpretations. On the other hand, if ''B'' is satisfiable, then there is an accepting computation for ''M'' on input ''I'' that follows the steps indicated by the assignments to the variables.
+There are ''O''(''p''(''n'')<sup>2</sup>) Boolean variables, each encodeable in space ''O''(log&nbsp;''p''(''n'')). The number of clauses is ''O''(''p''(''n'')<sup>3</sup>) so the size of ''B'' is ''O''(log(''p''(''n''))''p''(''n'')<sup>3</sup>). Thus the transformation is certainly a polynomial-time many-one reduction, as required.
+==Consequences==
+The proof shows that any problem in NP can be reduced in polynomial time (in fact, logarithmic space suffices) to an instance of the Boolean satisfiability problem. This means that if the Boolean satisfiability problem could be solved in polynomial time by a [[deterministic Turing machine]], then all problems in NP could be solved in polynomial time, and so the [[complexity class]] NP would be equal to the complexity class P.
+The significance of NP-completeness was made clear by the publication in 1972 of [[Richard Karp]]'s landmark paper, "Reducibility among combinatorial problems", in which he showed that [[Karp's 21 NP-complete problems|21 diverse combinatorial and graph theoretical problems]], each infamous for its intractability, are NP-complete.<ref name="Karp">{{cite book | last = Karp | first = Richard M. | authorlink = Richard Karp | chapter = Reducibility Among Combinatorial Problems | title = Complexity of Computer Computations | editor = Raymond E. Miller and James W. Thatcher (editors) | publisher = Plenum | location = New York | pages = 85–103 | year = 1972 | url = http://www.cs.berkeley.edu/~luca/cs172/karp.pdf | isbn=0-306-30707-3}}</ref>
+Karp showed each of his problems to be NP-complete by reducing another problem (already shown to be NP-complete) to that problem.  For example, he showed the problem 3SAT (the [[Boolean satisfiability problem]] for expressions in [[conjunctive normal form]] with exactly three variables or negations of variables per clause) to be NP-complete by showing how to reduce (in polynomial time) any instance of SAT to an equivalent instance of 3SAT.  (First you modify the proof of the Cook–Levin theorem, so that the resulting formula is in conjunctive normal form, then you introduce new variables to split clauses with more than 3 atoms.  For example, the clause (A ∨ B ∨ C ∨ D) can be replaced by the conjunction of clauses (A ∨ B ∨ Z) ∧ (¬Z ∨ C ∨ D), where Z is a new variable which will not be used anywhere else in the expression.  Clauses with fewer than 3 atoms can be padded; for example, A can be replaced by (A ∨ A ∨ A), and  (A ∨ B) can be replaced by (A ∨ B ∨ B) ).
+Garey and Johnson presented more than 300 NP-complete problems in their book ''Computers and Intractability: A Guide to the Theory of NP-Completeness'',<ref name="Garey"/> and new problems are still being discovered to be within that complexity class.
+Although many practical instances of SAT can be [[Boolean satisfiability problem#Algorithms for solving SAT|solved by heuristic methods]], the question of whether there is a deterministic polynomial-time algorithm for SAT (and consequently all other NP-complete problems) is still a famous unsolved problem, despite decades of intense effort by complexity theorists, mathematical logicians, and others.  For more details, see the article [[P=NP problem]].
+==References==
+{{reflist}}
+{{DEFAULTSORT:Cook-Levin theorem}}
+[[Category:Theorems in computational complexity theory]]
+[[Category:Articles containing proofs]]

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