From Petri Nets to Polynomials: Modeling, Algorithms, and Complexity (Abstract) (Invited Talk)

  • Ernst W. Mayr
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6244)

Abstract

Petri nets are a widely-used model for parallel and distributed systems of concurrent systems using common resources. They admit a precise algebraic formalization as vector addition or vector replacement systems. If one considers symmetric VRS’s, it turns out that they are equivalent to finitely presented commutative semigroups or to binomial ideals in a multivariate ring over ℚ.

We outline and survey the interaction between these domains of computational algebra, system modeling and verification, and, in particular, complexity theory. While many of the fundamental computational problems in these areas turn out to be very complex (i.e., EXPSPACE-complete or even worse, we also present some new results concerning better complexity for restricted subclasses of the problems.

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Ernst W. Mayr
    • 1
  1. 1.Institut für InformatikTechnische Universität MünchenGarchingGermany

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