Monomials in arithmetic circuits: Complete problems in the counting hierarchy

Fournier, Hervé; Malod, Guillaume; Mengel, Stefan

doi:10.4230/LIPIcs.STACS.2012.362

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Monomials in arithmetic circuits: Complete problems in the counting hierarchy

Authors Hervé Fournier, Guillaume Malod, Stefan Mengel

Part of: Volume: 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: Symposium on Theoretical Aspects of Computer Science (STACS)
License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
Publication Date: 2012-02-24

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LIPIcs.STACS.2012.362.pdf

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Document Identifiers

DOI: 10.4230/LIPIcs.STACS.2012.362
URN: urn:nbn:de:0030-drops-34240

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Keywords

arithmetic circuits
counting problems
polynomials

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Abstract

We consider the complexity of two questions on polynomials given by arithmetic circuits: testing whether a monomial is present and counting the number of monomials. We show that these problems are complete  for  subclasses of the counting hierarchy which had few or no known  natural complete problems before. We also study these questions for circuits computing multilinear polynomials.

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Hervé Fournier, Guillaume Malod, and Stefan Mengel. Monomials in arithmetic circuits: Complete problems in the counting hierarchy. In 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 14, pp. 362-373, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012) https://doi.org/10.4230/LIPIcs.STACS.2012.362

Author Details

Hervé Fournier

Guillaume Malod

Stefan Mengel

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