Satisfiability

Difficulty is measured in number recursive calls made by a DPLL algorithm. citation 3-satisfiability can be generalized to k-satisfiability (k-SAT, also k-CNF-SAT), when formulas in CNF are considered with each clause containing up to k literals.

As noted above, this is the Cook–Levin theorem ; its proof that satisfiability is NP-complete contains technical details about Turing machines as they relate to the definition of NP.

It can be seen as P's version of the Boolean satisfiability problem.

More recent Satisfiability Modulo Theories solvers use complete integer programming techniques to handle quantifier-free fragment of Presburger arithmetic theory (King, Barrett, Tinelli 2014).

Note that the tautology problem for positive Boolean formulae remains co-NP complete, even though the satisfiability problem is trivial, as every positive Boolean formula is satisfiable.

Particularly in hardware design and verification applications, satisfiability and other logical properties of a given propositional formula are sometimes decided based on a representation of the formula as a binary decision diagram (BDD).

The Boolean satisfiability problem is one of many such NP-complete problems.

The Boolean satisfiability problem (SAT) is, given a formula, to check whether it is satisfiable.

The membership in P of the satisfiability of 2CNF, Horn, and XOR-SAT formulae are special cases of this theorem.

The satisfiability problem is the problem of whether there are assignments of truth values to variables that make a Boolean expression true.

XOR-satisfiability Another special case is the class of problems where each clause contains XOR (i.e. exclusive or ) rather than (plain) OR operators.