NDLI: Narrow Proofs May Be Spacious:Separating Space and Width in Resolution

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Nordstrm, Jakob
Copyright Year	2009
Abstract	The width of a resolution proof is the maximal number of literals in any clause of the proof. The space of a proof is the maximal number of clauses kept in memory simultaneously if the proof is only allowed to infer new clauses from clauses currently in memory. Both of these measures have previously been studied and related to the resolution refutation size of unsatisfiable conjunctive normal form (CNF) formulas. Also, the minimum refutation space of a formula has been proven to be at least as large as the minimum refutation width, but it has been open whether space can be separated from width or the two measures coincide asymptotically. We prove that there is a family of k-CNF formulas for which the refutation width in resolution is constant but the refutation space is nonconstant, thus solving a problem mentioned in several previous papers.
Starting Page	59
Ending Page	121
Page Count	63
File Format	PDF
ISSN	00975397
DOI	10.1137/060668250
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	1 (Special Issue On The Thirty-Eighth Annual ACM Symposium On Theory Of Computing (STOC 2006))
Volume Number	39
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2009-05-28
Access Restriction	Subscribed
Subject Keyword	pebbling contradiction Computational difficulty of problems Mechanization of proofs and logical operations proof complexity lower bound resolution space Logic in computer science Complexity of proofs separation Theorem proving width pebble game
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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