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On polynomial ideals, their complexity, and applications

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Fundamentals of Computation Theory (FCT 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 965))

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Abstract

A polynomial ideal membership problem is a (w+1)-tuple P=(f, g 1 ,g 2 , ..., g w ) where f and the g i are multivariate polynomials over some ring, and the problem is to determine whether f is in the ideal generated by the g i . For polynomials over the integers or rationals, it is known that this problem is exponential space complete. We discuss complexity results known for a number of problems related to polynomial ideals, like the word problem for commutative semigroups, a quantitative version of Hilbert's Nullstellensatz, and the reachability and other problems for (reversible) Petri nets.

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  1. Institut für Informatik, Technische Universität München, D-80290, München, Germany

    Ernst W. Mayr

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  1. Ernst W. Mayr
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Horst Reichel

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© 1995 Springer-Verlag Berlin Heidelberg

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Mayr, E.W. (1995). On polynomial ideals, their complexity, and applications. In: Reichel, H. (eds) Fundamentals of Computation Theory. FCT 1995. Lecture Notes in Computer Science, vol 965. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60249-6_42

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  • DOI: https://doi.org/10.1007/3-540-60249-6_42

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  • Print ISBN: 978-3-540-60249-1

  • Online ISBN: 978-3-540-44770-2

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