Saving Space in a Time Efficient Simulation Algorithm

  • Authors:

  • Silvia Crafa;Francesco Ranzato;Francesco Tapparo

  • Affiliations:

  • (Correspd.) Dipartimento di Matematica Pura ed Applicata, University of Padova, Italy. {crafa, ranzato, tapparo}@math.unipd.it;Dipartimento di Matematica Pura ed Applicata, University of Padova, Italy. {crafa, ranzato, tapparo}@math.unipd.it;Dipartimento di Matematica Pura ed Applicata, University of Padova, Italy. {crafa, ranzato, tapparo}@math.unipd.it

  • Venue:
  • Fundamenta Informaticae - Application of Concurrency to System Design, the Eighth Special Issue
  • Year:
  • 2011

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Abstract

A number of algorithms for computing the simulation preorder on Kripke structures and on labelled transition systems are available. Among them, the algorithm by Ranzato and Tapparo [2007] has the best time complexity,while the algorithm by Gentilini et al. [2003] - successively corrected by van Glabbeek and Ploeger [2008] - has the best space complexity. Both space and time complexities are critical issues in a simulation algorithm, in particular memory requirements are crucial in the context of model checking when dealing with large state spaces. Here, we propose a new simulation algorithm that is obtained as a space saving modification of the time efficient algorithm by Ranzato and Tapparo: a symbolic representation of sets is embedded in this algorithm so that any set of states manipulated by the algorithm can be efficiently stored as a set of blocks of a suitable state partition. It turns out that this novel simulation algorithm has a space complexity comparable with Gentilini et al.'s algorithm while improving on Gentilini et al.'s time bound.