The Complexity of Resolution with Generalized Symmetry Rules

Stefan Szeider
2005 Theory of Computing Systems  
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more » ... out the formal permission of the copyright holders. Please consult the full DRO policy for further details. Abstract We generalize Krishnamurthy's well-studied symmetry rule for resolution systems by considering homomorphisms instead of symmetries; symmetries are injective maps of literals which preserve complements and clauses; homomorphisms arise from symmetries by releasing the constraint of being injective. We prove that the use of homomorphisms yields a strictly more powerful system than the use of symmetries by exhibiting an infinite sequence of sets of clauses for which the consideration of global homomorphisms allows exponentially shorter proofs than the consideration of local symmetries. It is known that local symmetries give rise to a strictly more powerful system than global symmetries; we prove a similar result for local and global homomorphisms. Finally, we obtain an exponential lower bound for the resolution system enhanced by the local homomorphism rule.
doi:10.1007/s00224-004-1192-0 fatcat:dqmy6qrixnb7tnyszw7qaugqsm