Matches in DBpedia 2014 for { ?s ?p #P-complete, pronounced "sharp P complete" or "number P complete" is a complexity class in computational complexity theory. By definition, 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. Equivalently, a problem is #P-complete if and only if it is in #P, and for any non-deterministic Turing machine ("NP machine"), the problem of computing its number of accepting paths can be reduced to this problem.Examples of #P-complete problems include: How many different variable assignments will satisfy a given general boolean formula? (#SAT) How many different variable assignments will satisfy a given DNF formula? How many different variable assignments will satisfy a given 2SAT formula? How many perfect matchings are there for a given bipartite graph? What is the value of the permanent of a given matrix whose entries are 0 or 1? (See Permanent is sharp-P-complete.) How many graph colorings using k colors are there for a particular graph G? How many different linear extensions are there for a given partial order, or, equivalently, how many different topological orderings are there for a given directed acyclic graph?A polynomial-time algorithm for solving a #P-complete problem, if it existed, would imply P = NP, and thus P = PH. No such algorithm is currently known.. }
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- Sharp-P-complete abstract "#P-complete, pronounced "sharp P complete" or "number P complete" is a complexity class in computational complexity theory. By definition, 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. Equivalently, a problem is #P-complete if and only if it is in #P, and for any non-deterministic Turing machine ("NP machine"), the problem of computing its number of accepting paths can be reduced to this problem.Examples of #P-complete problems include: How many different variable assignments will satisfy a given general boolean formula? (#SAT) How many different variable assignments will satisfy a given DNF formula? How many different variable assignments will satisfy a given 2SAT formula? How many perfect matchings are there for a given bipartite graph? What is the value of the permanent of a given matrix whose entries are 0 or 1? (See Permanent is sharp-P-complete.) How many graph colorings using k colors are there for a particular graph G? How many different linear extensions are there for a given partial order, or, equivalently, how many different topological orderings are there for a given directed acyclic graph?A polynomial-time algorithm for solving a #P-complete problem, if it existed, would imply P = NP, and thus P = PH. No such algorithm is currently known.".