X3SAT is Decidable in Time (original) (raw)

Abstract

We study the problem exact 3-SAT (X3SAT) for propositional formulas in conjunctive normal form (CNF) C = c 1 _ _ c m each clause c i containing at most three literals. Then C 2 X3SAT i there is a truth assignment t : V n ! f0; 1g; s.t. exactly one literal in each clause is set to true (1). The corresponding decision problem also is called X3SAT. As is well known problem X3SAT is NP-complete [5] and also XSAT as a generalization is NP-complete. By adapting and improving branching techniques like that in [4] we are able to prove that XSAT 2 O(2 thereby improving a more recent result found in [1] stating XSAT 2 O(2 ).

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