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Completeness results for reachability, containment, and equivalence, with respect to conflict-free vector replacement systems

  • Rodney R. Howell
  • Louis E. Rosier
Petri Nets, Algebraic Specification
Part of the Lecture Notes in Computer Science book series (LNCS, volume 267)

Abstract

In this paper, we give completeness results for the reachability, containment, and equivalence problems for conflict-free vector replacement systems (VRSs). We first give an NP algorithm for deciding reachability, thus giving the first primitive recursive algorithm for this problem. Since Jones, Landweber, and Lien have shown this problem to be NP-hard, it follows that the problem is NP-complete. Next, we show as our main result that the containment and equivalence problems are 2 P -complete, where 2 P is the set of all languages whose complements are in the second level of the polynomial-time hierarchy. In showing the upper bound, we first show that the reachability set has a semilinear set (SLS) representation that is exponential in the size of the problem description, but which has a high degree of symmetry. We are then able to utilize a strategy introduced by Huynh (concerning SLSs) to complete our upper bound proof.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Rodney R. Howell
    • 1
  • Louis E. Rosier
    • 1
  1. 1.Department of Computer SciencesUniversity of Texas at AustinAustin

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