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In complexity theory, the notion of P-complete decision problems is useful in the analysis of both: which problems are difficult to parallelize effectively, and; which problems are difficult to solve in limited space. Formally, a decision problem is P-complete if it is in P and that every problem in P can be reduced to it by using an appropriate reduction. The specific type of reduction used varies and may affect the exact set of problems. More information...

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    • In computational complexity theory, co-NP is a complexity class. A problem is a member of co-NP if and only if its complement is in complexity class NP. In simple terms, co-NP is the class of problems for which efficiently verifiable proofs of no instances, sometimes called counterexamples, exist.
    • In computational complexity theory, NP is one of the most fundamental complexity classes. The abbreviation NP refers to "nondeterministic polynomial time". Intuitively, NP is the set of all decision problems for which the 'yes'-answers have simple proofs of the fact that the answer is indeed 'yes'. More precisely, these proofs have to be verifiable in polynomial time by a deterministic Turing machine.
    • In complexity theory, the class NC (for "Nick's Class") is the set of decision problems decidable in polylogarithmic time on a parallel computer with a polynomial number of processors. In other words, a problem is in NC if there exist constants c and k such that it can be solved in time O(log n) using O(n) parallel processors. Stephen Cook coined the name "Nick's class" after Nick Pippenger, who had done extensive research on circuits with polylogarithmic depth and polynomial size.
    • In computational complexity theory, the complexity class #P (pronounced "sharp P" or "number P") is the set of the counting problems associated with the decision problems in the set NP. More formally, #P is the class of function problems of the form "compute ƒ(x)," where ƒ is the number of accepting paths of an NP machine. Unlike most well-known complexity classes, it is not a class of decision problems but a class of function problems.
    • #P-complete, pronounced "sharp P complete" or "number P complete" is a complexity class in computational complexity theory. A problem is #P-complete if and only if it is in #P, and every problem in #P can be reduced to it by a polynomial-time counting reduction, i.e. a polynomial-time Turing reduction relating the cardinalities of solution sets.
    • In computational complexity theory, PSPACE is the set of all decision problems which can be solved by a Turing machine using a polynomial amount of space.
    • In computational complexity theory, the complexity class NP-complete (abbreviated NP-C or NPC), is a class of problems having two properties: Any given solution to the problem can be verified quickly; the set of problems with this property is called NP (nondeterministic polynomial time). If the problem can be solved quickly (in polynomial time), then so can every problem in NP.
      http://en.wikipedia.org/wiki/File:Relative_NPC_chart.PNG
    • In complexity theory, computational problems that are co-NP-complete are those that are the hardest problems in co-NP, in the sense that they are the ones most likely not to be in P. If there exists a way to solve a co-NP-complete problem quickly, then that algorithm can be used to solve all co-NP problems quickly. Each Co-NP-complete problem is the complement of an NP-complete problem. The two sets are either equal or disjoint. The latter is thought more likely, but this is not known.
    • NP-hard, in computational complexity theory, is a class of problems that are, informally, "at least as hard as the hardest problems in NP". A problem H is NP-hard if and only if there is an NP-complete problem L that is polynomial time Turing-reducible to H (i.e. , L ≤ TH). In other words, L can be solved in polynomial time by an oracle machine with an oracle for H.
    • In complexity theory, a decision problem is PSPACE-complete if it is in the complexity class PSPACE, and every problem in PSPACE can be reduced to it in polynomial time. The problems that are PSPACE-complete can be thought of as the hardest problems in PSPACE. These problems are widely suspected to be outside of the more famous complexity classes P and NP, but that is not known. It is known that they lie outside of NC.

     

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