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The complexity of resolution refinements. (English) Zbl 1160.03005
Much of the research about the satisfiability problem has centered around the method of resolution [J. A. Robinson, “A machine-oriented logic based on the resolution principle”, J. Assoc. Comput. Mach. 12, 23–41 (1965; Zbl 0139.12303)]. This method can be applied to both propositional as well as higher-order theorem proving. Resolution algoritms take as input a formula \(F\) and output a resolution refutation of \(F\) if and only if \(F\) is unsatisfiable. Several variants and refinements of resolution have been investigated in order to determine which particular variant is most efficient for generating resolution refutations. In this paper, the author studies the most popular refinements of resolution and provides a characterization of the relative complexity of these approaches.

MSC:
03B35 Mechanization of proofs and logical operations
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