Some Complexity Results for Prefix Gröbner Bases in Free Monoid Rings

  • Andrea Sattler-Klein
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4639)

Abstract

We establish the following complexity results for prefix Gröbner bases in free monoid rings: 1. \(|{\cal R}| \cdot size(p)\) reduction steps are sufficient to normalize a given polynomial p w.r.t. a given right-normalized system \({\cal R}\) of prefix rules compatible with some total admissible wellfounded ordering >. 2. \(O(|{\cal R}|^2 \cdot size({\cal R}))\) basic steps are sufficient to transform a given terminating system \({\cal R}\) of prefix rules into an equivalent right-normalized system. 3. \(O(|{\cal R}|^3 \cdot size({\cal R}))\) basic steps are sufficient to decide whether or not a given terminating system \({\cal R}\) of prefix rules is a prefix Gröbner basis. The latter result answers an open question posed by Zeckzer in [10].

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Andrea Sattler-Klein
    • 1
  1. 1.Technische Universität Kaiserslautern, Fachbereich Informatik, Postfach 3049, 67653 KaiserslauternGermany

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