Universal Relations and #P-Completeness
نویسندگان
چکیده
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.
منابع مشابه
Remarks on completeness of lattice-valued Cauchy spaces
We study different completeness definitions for two categories of lattice-valued Cauchy spaces and the relations between these definitions. We also show the equivalence of a so-called completion axiom and the existence of a completion.
متن کاملAn investigation on regular relations of universal hyperalgebras
In this paper, by considering the notion of $Sigma$-hyperalgebras for an arbitrary signature $Sigma$, we study the notions of regular and strongly regular relations on a $Sigma$-hyperalgebra, $mathfrak{A}$. We show that each regular relation which contains a strongly regular relation is a strongly regular relation. Then we concentrate on the connection between the fundamental relation of $mathf...
متن کاملDownward-directed transitive frames with universal relations
In this paper we identify modal logics of some bimodal Kripke frames corresponding to geometrical structures. Each of these frames is a set of ‘geometrical’ objects with some natural accessibility relation plus the universal relation. For these logics we present finite axiom systems and prove completeness. We also show that all these logics have the finite model property and are PSPACE-complete...
متن کاملCharacterization of fuzzy complete normed space and fuzzy b-complete set
The present paper introduces the notion of the complete fuzzy norm on a linear space. And, some relations between the fuzzy completeness and ordinary completeness on a linear space is considered, moreover a new form of fuzzy compact spaces, namely b-compact spaces and b-closed spaces are introduced. Some characterizations of their properties are obtained.
متن کاملUniversal P Systems: One Catalyst Can Be Sufficient
Whether P systems with only one catalyst can already be universal, is still an open problem. Here we establish universality (computational completeness) by using specific variants of additional control mechanisms. At each step using only multiset rules from one set of a finite number of sets of rules allows for obtaining computational completeness with one catalyst and only one membrane. If the...
متن کامل