NP-Completeness of Refutability by Literal-Once Resolution

Authors:
Stefan Szeider
Affiliations:
-
Venue:
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Year:
2001

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Abstract

A boolean formula in conjunctive normal form (CNF) F is refuted by literal-once resolution if the empty clause is inferred from F by resolving on each literal of F at most once. Literal-once resolution refutations can be found nondeterministically in polynomial time, though this restricted system is not complete. We show that despite of the weakness of literal-once resolution, the recognition of CNF-formulas which are refutable by literal-once resolution is NP-complete. We study the relationship between literal-once resolution and read-once resolution (introduced by Iwama and Miyano). Further we answer a question posed by Kullmann related to minimal unsatisfiability.