On subclasses of minimal unsatisfiable formulas

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• 作者：Bü ; ning ; Hans Kleine
• 关键词：Propositional formulas ; Minimal unsatisfiability
• 刊名：Discrete Applied Mathematics
• 出版年：2000
• 出版时间：December 21, 2000
• 年：2000
• 卷：107
• 期：1-3
• 页码：83-98
• 全文大小：126 K

文摘

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.