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arXiv · 1401.8046

Universal First-Order Logic is Superfluous for NL, P, NP and coNP

Nerio Borges·Blai Bonet
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Abstract

In this work we continue the syntactic study of completeness that began with the works of Immerman and Medina. In particular, we take a conjecture raised by Medina in his dissertation that says if a conjunction of a second-order and a first-order sentences defines an NP-complete problems via fops, then it must be the case that the second-order conjoint alone also defines a NP-complete problem. Although this claim looks very plausible and intuitive, currently we cannot provide a definite answer for it. However, we can solve in the affirmative a weaker claim that says that all ``consistent'' universal first-order sentences can be safely eliminated without the fear of losing completeness. Our methods are quite general and can be applied to complexity classes other than NP (in this paper: to NLSPACE, PTIME, and coNP), provided the class has a complete problem satisfying a certain combinatorial property.

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Nerio Borges, Blai Bonet. 2014-02-28. Universal First-Order Logic is Superfluous for NL, P, NP and coNP. https://doi.org/10.2168/lmcs-10(1%3A15)2014

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