The complexity of the coverability, the containment, and the equivalence problems for commutative semigroups

  • Ulla Koppenhagen
  • Ernst W. Mayr
Technical Contributions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1279)


In this paper, we present optimal decision procedures for the coverability, the containment, and the equivalence problems for commutative semigroups. These procedures require at most space 2c·n, where n is the size of the problem instance, and c is some problem independent constant. Our results close the gap between the 2c′-n-log-n space upper bound, shown by Rackoff for the coverability problem and shown by Huynh for the containment and the equivalence problems, and the exponential space lower bound resulting from the corresponding bound for the uniform word problem established by Mayr and Meyer.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Ulla Koppenhagen
    • 1
  • Ernst W. Mayr
    • 1
  1. 1.Institut für InformatikTechnische Universität MünchenMünchenGermany

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