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2-satisfiability




:(x_{11} \lor x_{12}) \land (x_{21} \lor x_{22}) \land \cdots \land (x_{n1} \lor x_{n2}) \land \cdots

where \lor means OR, \land means AND, each x is a variable, with or without a NOT in front of it, and each variable can appear multiple times in the expression.

Unlike general Satisfiability or 3-satisfiability which are NP-complete and have no known efficient Algorithm , 2-satisfiability can be solved in Polynomial Time . There are several known polynomial time algorithms for 2-SAT, for example, based on Resolution or Random Walk s. More powerfully, 2-satisfiability is NL-complete (Papadimitriou 1994, Thrm. 16.3), meaning that it is one of the "hardest" or "most expressive" problems which can be solved in nondeterministic logspace ( NL ).

A related problem is maximum-2-satisfiability (MAX-2-SAT) in which the input is still a 2-CNF but we have to determine the maximum number of clauses that can be simultaneously satisfied by an assignment. MAX-2-SAT is a particular case of Maximum-satisfiability . It is NP-complete .


REFERENCES



  • Christos H. Papadimitriou. Computational Complexity (''chapter 4.2''). Addison-Wesley, 1994. ISBN 0-201-53082-1