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

Extended Abstract
  • Zhe Dang
  • Oscar H. Ibarra
  • Pierluigi San Pietro
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2245)

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 reversalbounded counters and a free counter.

Keywords

Model Check Mode Vector Disjunctive Normal Form Reachability Problem Time Automaton 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Zhe Dang
    • 1
  • Oscar H. Ibarra
    • 2
  • Pierluigi San Pietro
    • 3
  1. 1.School of Electrical Engineering and Computer ScienceWashington State UniversityPullman
  2. 2.Department of Computer ScienceUniversity of CaliforniaSanta Barbara
  3. 3.Dipartimento di Elettronica e InformazionePolitecnico di MilanoItalia

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