Thomson problem

In computability theory and computational complexity theory, RE (recursively enumerable) is the class of decision problems for which a 'yes' answer can be verified by a Turing machine in a finite amount of time.^[1] Informally, it means that if the answer is 'yes', then there is some procedure which takes finite time to determine this. On the other hand, if the answer is 'no', the machine might never halt. Equivalently, RE is the class of decision problems for which a Turing machine can list all the 'yes' instances, one by one (this is what 'enumerable' means).

Similarly, co-RE is the set of all languages that are complements of a language in RE. In a sense, co-RE contains languages of which membership can be disproved in a finite amount of time, but proving membership might take forever.

Each member of RE is a recursively enumerable set and therefore a Diophantine set.

Relations to other classes

The set of recursive languages (R) is a subset of both RE and co-RE.^[2] In fact, it is the intersection of those two classes, because we can decide any problem for which there exists a recogniser and also a co-recogniser by simply interleaving them until one obtains a result. Therefore:

{\mbox{R}}={\mbox{RE}}\cap {\mbox{co-RE}}.

RE-complete

RE-complete is the set of decision problems that are complete for RE. In a sense, these are the "hardest" recursively enumerable problems. All such problems are nonrecursive. Generally, no constraint is placed on the reductions used except that they must be many-one reductions.

Examples of RE-complete problems:

Halting problem: Whether a program given a finite input finishes running or will run forever.
By Rice's Theorem, deciding membership in any nontrivial subset of the set of recursive functions is RE-hard. It will be complete whenever the set is recursively enumerable.
Template:Harvs^[3] has proven that all creative sets are RE-complete.
The uniform word problem for groups or semigroups. [Indeed, the word problem for some individual groups is RE-complete.]
Deciding membership in a general unrestricted formal grammar. [Again, certain individual grammars have RE-complete membership problem.]
The validity problem for first-order logic.
Post correspondence problem: Given a finite set of strings, determine if there is a string that can be factored into a composition of the strings (allowing repeats) in two different ways.
Determining if a Diophantine equation has any integer solutions.

co-RE-complete

co-RE-complete is the set of decision problems that are complete for co-RE. In a sense, these are the complements of the hardest recursively enumerable problems.

Examples of co-RE-complete problems:

The Domino Problem for Wang tiles.
The satisfiability problem for first-order logic

References

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[1] Template:CZoo

[2] Template:CZoo

[3] 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.

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[2]

[3]

Thomson problem

Contents

Relations to other classes

RE-complete

co-RE-complete

See also

References

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Thomson problem

Relations to other classes

RE-complete

co-RE-complete

See also

References

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