A syntactic characterization of NP-completeness

A syntactic characterization of NP-completeness

Fagin (1974) proved that NP is equal to the set of problems expressible in second-order existential logic (SO/spl exist/). We consider problems that are NP-complete via first-order projections (fops). These low-level reductions are known to have nice properties, including the fact that every pair of...

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Hauptverfasser: Medina, J.A., Immerman, N.
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Logic
NP-complete problem
Sufficient conditions
Vocabulary
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description Fagin (1974) proved that NP is equal to the set of problems expressible in second-order existential logic (SO/spl exist/). We consider problems that are NP-complete via first-order projections (fops). These low-level reductions are known to have nice properties, including the fact that every pair of problems that are NP-complete via fops are isomorphic via a first-order definable isomorphism (E. Allender et al., 1993). However, before this paper, fewer than five natural problems had actually been shown to be NP-complete via fops. We give a necessary and sufficient syntactic condition for an SO/spl exist/ formula to represent a problem that is NP-complete via fops. Using this condition we prove syntactically that 29 natural NP-complete problems remain complete via fops.< >
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subjects Computer science
Logic
NP-complete problem
Sufficient conditions
Vocabulary
title A syntactic characterization of NP-completeness
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