Abstract
An algorithm for satisfiability testing in the propositional calculus with a worst case running time that grows at a rate less than 2(.25+ε)L is described, where L can be either the length of the input expression or the number of occurrences of literals (i.e., leaves) in it. This represents a new upper bound on the complexity of non-clausal satisfiability testing. The performance is achieved by using lemmas concerning assignments and pruning that preserve satisfiability, together with choosing a “good” variable upon which to recur. For expressions in clause form, it is shown that the Davis-Putnam procedure satisfies the same upper bound.
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Van Gelder, A. (1984). A Satisfiability Tester for Non-Clausal Propositional Calculus. In: Shostak, R.E. (eds) 7th International Conference on Automated Deduction. CADE 1984. Lecture Notes in Computer Science, vol 170. Springer, New York, NY. https://doi.org/10.1007/978-0-387-34768-4_6
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DOI: https://doi.org/10.1007/978-0-387-34768-4_6
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