Liveness Verification of Reversal-Bounded Multicounter Machines with a Free Counter

  • Authors:
  • Zhe Dang;Oscar H. Ibarra;Pierluigi San Pietro

  • Affiliations:
  • -;-;-

  • Venue:
  • FST TCS '01 Proceedings of the 21st Conference on Foundations of Software Technology and Theoretical Computer Science
  • Year:
  • 2001

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Abstract

We investigate the Presburger liveness problems for nondeterministic reversal-bounded multicounter machines with a free counter (NCMFs). We show the following: - The ∃-Presburger-i.o. problem and the ∃-Presburger-eventual problem are both decidable. So are their duals, the ∀-Presburger-almost-always problem and the ∀-Presburger-always problem. - The ∀-Presburger-i.o. problem and the ∀-Presburger-eventual problem are both undecidable. So are their duals, the ∃-Presburger-almost-always problem and the ∃-Presburger-always problem. These results can be used to formulate a weak form of Presburger linear temporal logic and developits model-checking theories for NCMFs. They can also be combined with [12] to study the same set of liveness problems on an extended form of discrete timed automata containing, besides clocks, a number of reversal-bounded counters and a free counter.