Exact 3-satisfiability is decidable in time O(2(0.16254n))
Let F = C-1 boolean AND...boolean AND C-m be a Boolean formula in conjunctive normal form over a set V of n propositional variables, s.t. each clause C-i contains at most three literals l over V. Solving the problem exact 3-satisfiability (X3SAT) for F means to decide whether there is a truth assignment setting exactly one literal in each clause of F to true ( 1). As is well known X3SAT is NP-complete [6]. By exploiting a perfect matching reduction we prove that X3SAT is deterministically decidable in time O(2(0.18674n)). Thereby we improve a result in [2,3] stating X3SAT is an element of O(2(0.2072n)) and a bound of O(2(0.200002n)) for the corresponding enumeration problem # X3SAT stated in a preprint [1]. After that by a more involved deterministic case analysis we are able to show that X3SAT. O(2(0.16254n)).
np-completeness perfect matching exact satisfiability autonomous clause pattern formula graph