Correcting a Space-Efficient Simulation Algorithm

  • Authors:
  • Rob Glabbeek;Bas Ploeger

  • Affiliations:
  • National ICT Australia, Sydney, Australia NSW1466 and School of Computer Science and Engineering, The University of New South Wales, Sydney, Australia NSW 2052;Design and Analysis of Systems Group, Eindhoven University of Technology, Eindhoven, The Netherlands 5600 MB

  • Venue:
  • CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
  • Year:
  • 2008

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Abstract

Although there are many efficient algorithms for calculating the simulation preorder on finite Kripke structures, only two have been proposed of which the space complexity is of the same order as the size of the output of the algorithm. Of these, the one with the best time complexity exploits the representation of the simulation problem as a generalised coarsest partition problem. It is based on a fixed-point operator for obtaining a generalised coarsest partition as the limit of a sequence of partition pairs. We show that this fixed-point theory is flawed, and that the algorithm is incorrect. Although we do not see how the fixed-point operator can be repaired, we correct the algorithm without affecting its space and time complexity.