DP Lower bounds for equivalence-checking and model-checking of one-counter automata

  • Authors:

  • Petr Jančar;Antonín Kučera;Faron Moller;Zdeněk Sawa

  • Affiliations:

  • Department of Computer Science, FEI, Technical University of Ostrava, 17. listopadu 15, Ostrava CZ-70833, Czech Republic;Faculty of Informatics, Masaryk University, Botanická 68a, Brno CZ-60200, Czech Republic;Department of Computer Science, University of Wales Swansea, Singleton Park, Swansea, Wales SA2 8PP, UK;Department of Computer Science, FEI, Technical University of Ostrava, 17. listopadu 15, Ostrava CZ-70833, Czech Republic

  • Venue:
  • Information and Computation
  • Year:
  • 2004

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Abstract

We present a general method for proving DP-hardness of problems related to formal verification of one-counter automata. For this we show a reduction of the SAT-UNSAT problem to the truth problem for a fragment of (Presburger) arithmetic. The fragment contains only special formulas with one free variable, and is particularly apt for transforming to simulation-like equivalences on one-counter automata. In this way we show that the membership problem for any relation subsuming bisimilarity and subsumed by simulation preorder is DP-hard (even) for one-counter nets (where the counter cannot be tested for zero). We also show DP-hardness for deciding simulation between one-counter automata and finite-state systems (in both directions), and for the model-checking problem with one-counter nets and the branching-time temporal logic EF.