On subclasses of minimal unsatisfiable formulas

Abstract We consider the minimal unsatisfiablity problem MU ( k ) for propositional formulas in conjunctive normal form (CNF) over n variables and n + k clauses, where k is fixed. k is called the difference. Any formula in MU ( k ) can be split into two minimal unsatisfiable formula. For such splittings we investigate the size of the differences of the resulting formulas in comparison to the difference of the initial formula. Based on these results we prove that MU ( k ) for fixed k is in NP, and for MU (2) we present a simple and unique characterization.