Lawler's algorithm: Difference between revisions

Latest revision as of 23:37, 29 May 2013

High-order logic is an extension of first-order and second-order with high order quantifiers. In descriptive complexity we can see that it is equal to the ELEMENTARY functions.^[1] There is a relation between the $i$ th order and non determinist algorithm the time of which is with $i-1$ level of exponentials.

Definitions and notations

We define high-order variable, a variable of order $i>1$ has got an arity $k$ and represent any set of $k$ -tuples of elements of order $i-1$ . They are usually written in upper-case and with a natural number as exponent to indicate the order. High order logic is the set of FO formulae where we add quantification over higher-order variables, hence we will use the terms defined in the FO article without defining them again.

HO $^{i}$ is the set of formulae where variable's order are at most $i$ . HO $_{j}^{i}$ is the subset of the formulae of the form $\phi =\exists {\overline {X_{1}^{i}}}\forall {\overline {X_{2}^{i}}}\dots Q{\overline {X_{j}^{i}}}\psi$ where $Q$ is a quantifier, $Q{\overline {X^{i}}}$ means that ${\overline {X^{i}}}$ is a tuple of variable of order $i$ with the same quantification. So it is the set of formulae with $j$ alternations of quantifiers of $i$ th order, beginning by and $\exists$ , followed by a formula of order $i-1$ .

Using the tetration's standard notation, $\exp _{2}^{0}(x)=x$ and $\exp _{2}^{i+1}(x)=2^{\exp _{2}^{i}(x)}$ . $\exp _{2}^{i+1}(x)=2^{2^{2^{2^{\dots ^{2^{x}}}}}}$ with $i$ times $2$

Property

Normal form

Every formula of $i$ th order is equivalent to a formula in prenex normal form, where we first write quantification over variable of $i$ th order and then a formula of order $i-1$ in normal form.

Relation to complexity classes

HO is equal to ELEMENTARY functions. To be more precise, ${\text{HO}}_{0}^{i}={\text{NTIME}}(\exp _{2}^{i-2}(n^{O(1)}))$ , it means a tower of $(i-2)$ 2s, ending with $n^{c}$ where $c$ is a constant. A special case of it is that $\exists {}SO$ =HO $_{0}^{2}$ =NTIME( $n^{O(1)}$ )=NP, which is exactly the Fagin's theorem. Using oracle machines in the polynomial hierarchy, HO $_{j}^{i}$ =NTIME( $\exp _{2}^{i-2}(n^{O(1)})^{\Sigma _{j}^{\rm {P}}}$ )

References

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External links

zoo about HO.

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[1] Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010

[1]

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+High-order logic is an extension of [[FO (complexity)|first-order]] and [[SO (complexity)|second-order]] with high order quantifiers. In [[descriptive complexity]] we can see that it is equal to the [[ELEMENTARY]] functions.<ref>{{Citation | author = Lauri Hella and José María Turull-Torres | title =Computing queries with higher-order logics | journal =Theoretical Computer Science | volume = 355 | edition= (what is called "number" in bibtex) | issue = 2 | year = 2006 | pages = 197&ndash;214   | issn =0304-3975 | publisher =Elsevier Science Publishers Ltd. | place =  Essex, UK | url = http://portal.acm.org/citation.cfm?id=1142890.1142897}}</ref> There is a relation between the <math>i</math>th order and non determinist algorithm the time of which is with <math>i-1</math> level of exponentials.
+== Definitions and notations ==
+We define high-order variable, a variable of order <math>i>1</math> has got an arity <math>k</math> and represent any set of <math>k</math>-[[tuple]]s of elements of order <math>i-1</math>. They are usually written in upper-case and with a natural number as exponent to indicate the order. High order logic is the set of [[FO (complexity)|FO]] formulae where we add quantification over higher-order variables, hence we will use the terms defined in the [[FO (complexity)|FO]] article without defining them again.
+HO<math>^i</math> is the set of formulae where variable's order are at most <math>i</math>. HO<math>^i_j</math> is the subset of the formulae of the form <math>\phi=\exists \overline{X^i_1}\forall\overline{X_2^i}\dots Q \overline{X_j^i}\psi</math> where <math>Q</math> is a quantifier, <math>Q \overline{X^i}</math> means that <math>\overline{X^i}</math> is  a tuple of variable of order <math>i</math> with the same quantification. So it is the set of formulae with <math>j</math> alternations of quantifiers of <math>i</math>th order, beginning by and <math>\exists</math>, followed by a formula of order <math>i-1</math>.
+Using the [[Tetration#Notation|tetration]]'s standard notation, <math>\exp_2^0(x)=x</math> and <math> \exp_2^{i+1}(x)=2^{\exp_2^{i}(x)}</math>. <math> \exp_2^{i+1}(x)=2^{2^{2^{2^{\dots^{2^{x}}}}}}</math> with <math>i</math> times <math>2</math>
+== Property ==
+===Normal form===
+Every formula of <math>i</math>th order is equivalent to a formula in prenex normal form, where we first write quantification over variable of <math>i</math>th order and then a formula of order <math>i-1</math> in normal form.
+=== Relation to complexity classes===
+HO is equal to [[ELEMENTARY]] functions.  To be more precise, <math>\text{HO}^i_0 = \text{NTIME}(\exp_2^{i-2}(n^{O(1)}))</math>, it means a tower of <math>(i-2)</math>  2s, ending with <math>n^c</math> where <math>c</math> is a constant. A special case of it is that <math>\exists{}SO</math>=HO<math>^2_0</math>=NTIME(<math>n^{O(1)}</math>)=[[NP (complexity)|NP]], which is exactly the [[Fagin's theorem]]. Using [[oracle machine]]s in the [[polynomial hierarchy]], HO<math>^i_j</math>=[[NTIME]](<math>\exp_2^{i-2}(n^{O(1)})^{\Sigma_j^{\rm P}}</math>)
+==References==
+{{Reflist}}
+==External links==
+* [http://qwiki.stanford.edu/wiki/Complexity_Zoo:H#ho|Complexity zoo about HO].
+[[Category:Finite model theory]]
+[[Category:Descriptive complexity]]
+[[Category:Computational complexity theory]]

Lawler's algorithm: Difference between revisions

Latest revision as of 23:37, 29 May 2013

Contents

Definitions and notations

Property

Normal form

Relation to complexity classes

References

External links

Navigation menu

Lawler's algorithm: Difference between revisions

Latest revision as of 23:37, 29 May 2013

Definitions and notations

Property

Normal form

Relation to complexity classes

References

External links

Navigation menu

Search