An Application of Matroid Theory to the SAT Problem
نویسنده
چکیده
We consider the deficiency and the maximal deficiency "! #$ % of a clauseset (a conjunctive normal form), where is the number of clauses in and is the number of variables. Combining ideas from matching and matroid theory with techniques from the area of resolution refutations, we prove that for clause-sets with '& ( , where ( is considered as a constant, the SAT problem, the minimally unsatisfiability problem and the MAXSAT problem are decidable in polynomial time (previously, only poly-time decidability of the minimally unsatisfiability problem was known, and that only for ( *) ).
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