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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This paper follows the methodology introduced by Agrawal and Biswas in [Manindra Agrawal, Somenath Biswas, Universal relations, in: Structure in Complexity Theory Conference, 1992, pp. 207-220], 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.