On Canonical Forms of Complete Problems via First-order Projections

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dc.creatorBorges, Nerio
dc.creatorBonet, Blai
dc.date2007-06-22
dc.date.accessioned2026-07-07T08:12:04Z
dc.date.available2026-07-07T08:12:04Z
dc.descriptionThe class of problems complete for NP via first-order reductions is known to be characterized by existential second-order sentences of a fixed form. All such sentences are built around the so-called generalized IS-form of the sentence that defines Independent-Set. This result can also be understood as that every sentence that defines a NP-complete problem P can be decomposed in two disjuncts such that the first one characterizes a fragment of P as hard as Independent-Set and the second the rest of P. That is, a decomposition that divides every such sentence into a quotient and residue modulo Independent-Set. In this paper, we show that this result can be generalized over a wide collection of complexity classes, including the so-called nice classes. Moreover, we show that such decomposition can be done for any complete problem with respect to the given class, and that two such decompositions are non-equivalent in general. Interestingly, our results are based on simple and well-known properties of first-order reductions.ow that this result can be generalized over a wide collection of complexity classes, including the so-called nice classes. Moreover, we show that such decomposition can be done for any complete problem with respect to the given class, and that two such decompositions are non-equivalent in general. Interestingly, our results are based on simple and well-known properties of first-order reductions.
dc.description9 pages
dc.identifierhttps://arxiv.org/abs/0706.3412
dc.identifierhttp://arxiv.org/abs/0706.3412
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/132326
dc.subjectComputational Complexity
dc.titleOn Canonical Forms of Complete Problems via First-order Projections
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