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Circuit satisfiability problem; Conjunctive Boolean query [3]: SR31 Cyclic ordering [36] Exact cover problem. Remains NP-complete for 3-sets. Solvable in polynomial time for 2-sets (this is a matching). [2] [3]: SP2 Finding the global minimum solution of a Hartree-Fock problem [37] Upward planarity testing [8] Hospitals-and-residents problem ...
An individual computational problem is thus associated with a particular family of Boolean circuits ,, … where each is the circuit handling inputs of n bits. A uniformity condition is often imposed on these families, requiring the existence of some possibly resource-bounded Turing machine that, on input n , produces a description of the ...
NP is the set of decision problems for which the problem instances, where the answer is "yes", have proofs verifiable in polynomial time by a deterministic Turing machine, or alternatively the set of problems that can be solved in polynomial time by a nondeterministic Turing machine. [2]
If the circuit C outputs A∧B for circuits A and B, join the branching programs that γ-compute A, δ-compute B, γ −1-compute A, and δ −1-compute B for a choice of 5-cycles γ and δ such that their commutator ε=γδγ −1 δ −1 is also a 5-cycle. (The existence of such elements was established in Lemma 2.)
The comparator circuit value problem (CCVP) is the problem of evaluating a comparator circuit given an encoding of the circuit and the input to the circuit. The complexity class CC is defined as the class of problems logspace reducible to CCVP. [1] An equivalent definition [2] is the class of problems AC 0 reducible to CCVP.
P-complete problems may be solvable with different time complexities. For instance, the Circuit Value Problem can be solved in linear time by a topological sort. Of course, because the reductions to a P-complete problem may have different time complexities, this fact does not imply that all the problems in P can also be solved in linear time.
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The first complete class to be defined and the most well known is NP-complete, a class that contains many difficult-to-solve problems that arise in practice. Similarly, a problem hard for a class C is called C-hard, e.g. NP-hard. Normally, it is assumed that the reduction in question does not have higher computational complexity than the class ...