Note: The NP-hardness of finding a directed acyclic graph for regular resolution

Authors:
Samuel R. Buss;Jan Hoffmann
Affiliations:
Department of Mathematics, University of California, San Diego, La Jolla, CA 92093-0112, USA;Department of Mathematics, University of California, San Diego, La Jolla, CA 92093-0112, USA
Venue:
Theoretical Computer Science
Year:
2008

Citing 8
Cited 1

Regular resolution versus unrestricted resolution

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Regular resolution lower bounds for the weak pigeonhole principle

STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
An exponential separation between regular and general resolution

STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
On the Relative Complexity of Resolution Refinements and Cutting Planes Proof Systems

SIAM Journal on Computing
Complexity of Finding Short Resolution Proofs

MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
NP-Completeness of Refutability by Literal-Once Resolution

IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Intriactability of Read-Once Resolution

SCT '95 Proceedings of the 10th Annual Structure in Complexity Theory Conference (SCT'95)
Resolution is Not Automatizable Unless W[P] is Tractable

FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science

Note: Finding a tree structure in a resolution proof is NP-complete

Theoretical Computer Science

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Abstract

Let R be a resolution refutation, given as a sequence of clauses without explicit description of the underlying dag. Then, it is NP-complete to decide whether R is a regular resolution refutation.