On Presburger Liveness of Discrete Timed Automata

  • Zhe Dang
  • Pierluigi San Pietro
  • Richard A. Kemmerer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2010)


Using an automata-theoretic approach, we investigate the decidability of liveness properties (called Presburger liveness properties) for timed automata when Presburger formulas on configurations are allowed. While the general problem of checking a temporal logic such as TPTL augmented with Presburger clock constraints is undecidable, we show that there are various classes of Presburger liveness properties which are decidable for discrete timed automata. For instance, it is decid- able, given a discrete timed automaton A and a Presburger property P, whether there exists an ω-path of A where P holds infinitely often. We also show that other classes of Presburger liveness properties are indeed undecidable for discrete timed automata, e.g., whether P holds infinitely often for each ω-path of A. These results might give insights into the cor- responding problems for timed automata over dense domains, and help in the definition of a fragment of linear temporal logic, augmented with Presburger conditions on configurations, which is decidable for model checking timed automata.


Model Check Temporal Logic Linear Temporal Logic Liveness Property 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
  • Pierluigi San Pietro
    • 2
  • Richard A. Kemmerer
    • 3
  1. 1.School of Electrical Engineering and Computer ScienceWashington State UniversityPullmanUSA
  2. 2.Dipartimento di Elettronica e InformazionePolitecnico di MilanoItalia
  3. 3.Department of Computer ScienceUniversity of California at Santa BarbaraUSA

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