A Dichotomy Theorem for Polynomial Evaluation

Irénée Briquel; Pascal Koiran

doi:10.1007/978-3-642-03816-7

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arXiv · 0902.2300

A Dichotomy Theorem for Polynomial Evaluation

Irénée Briquel·Pascal Koiran

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Abstract

A dichotomy theorem for counting problems due to Creignou and Hermann states that or any nite set S of logical relations, the counting problem #SAT(S) is either in FP, or #P-complete. In the present paper we show a dichotomy theorem for polynomial evaluation. That is, we show that for a given set S, either there exists a VNP-complete family of polynomials associated to S, or the associated families of polynomials are all in VP. We give a concise characterization of the sets S that give rise to "easy" and "hard" polynomials. We also prove that several problems which were known to be #P-complete under Turing reductions only are in fact #P-complete under many-one reductions.

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BibTeX RIS

Irénée Briquel, Pascal Koiran. 2009-12-15. A Dichotomy Theorem for Polynomial Evaluation. https://doi.org/10.1007/978-3-642-03816-7

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