On the complexity of checking semantic equivalences between pushdown processes and finite-state processes

  • Authors:

  • Antonín Kučera;Richard Mayr

  • Affiliations:

  • Faculty of Informatics, Masaryk University, Botanická 68a, 60200 Brno, Czech Republic;School of Informatics, LFCS, University of Edinburgh, 10 Crichton Street, Edinburgh EH8 9AB, UK

  • Venue:
  • Information and Computation
  • Year:
  • 2010

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Abstract

Simulation preorder/equivalence and bisimulation equivalence are the most commonly used equivalences in concurrency theory. Their standard definitions are often called strong simulation/bisimulation, while weak simulation/bisimulation abstracts from internal @t-actions. We study the computational complexity of checking these strong and weak semantic preorders/equivalences between pushdown processes and finite-state processes. We present a complete picture of the computational complexity of these problems and also study fixed-parameter tractability in two important input parameters: x, the size of the finite control of the pushdown process, and y, the size of the finite-state process. All simulation problems are generally EXPTIME-complete and only become polynomial if both parameters x and y are fixed. Weak bisimulation equivalence is PSPACE-complete, but becomes polynomial if and only if parameter x is fixed. Strong bisimulation equivalence is PSPACE-complete, but becomes polynomial if either parameter x or y is fixed.