Universal relations and #p-completeness

Authors:
Hervé Fournier;Guillaume Malod
Affiliations:
Laboratoire PRiSM, Université de Versailles, St-Quentin en Yvelines, France;Laboratory of Prof. Masahiko SATO, Graduate School of Informatics, Kyoto University, Japan
Venue:
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
Year:
2006

Citing 3
Cited 0

Structural complexity 1

Structural complexity 1
PP is as hard as the polynomial-time hierarchy

SIAM Journal on Computing
Universal resolutions for NP-complete problems

Theoretical Computer Science

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Abstract

This paper follows the methodology introduced by Agrawal and Biswas in [AB92], based on a notion of universality for the relations associated with NP-complete problems. The purpose was to study NP-complete problems by examining the effects of reductions on the solution sets of the associated witnessing relations. This provided a useful criterion for NP-completeness while suggesting structural similarities between natural NP-complete problems. We extend these ideas to the class #P. The notion we find also yields a practical criterion for #P-completeness, as illustrated by a varied set of examples, and strengthens the argument for structural homogeneity of natural complete problems.