Variable minimal unsatisfiability

Authors:
Zhenyu Chen;Decheng Ding
Affiliations:
Department of Mathematics, Nanjing University, China;Department of Mathematics, Nanjing University, China
Venue:
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
Year:
2006

Citing 15
Cited 2

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Abstract

In this paper, we present variable minimal unsatisfiability (VMU), which is a generalization of minimal unsatisfiability (MU). A characterization of a VMU formula F is that every variable of F is used in every resolution refutation of F. We show that the class of VMU formulas is DP-complete. For fixed deficiency (the difference of the number of clauses and the number of variables), the VMU formulas can be solved in polynomial time. Furthermore, we investigate more subclasses of VMU formulas. Although the theoretic results on VMU and MU are similar, some observations are shown that the extraction of VMU may be more practical than MU in some cases.