When Model-Checking Freeze LTL over Counter Machines Becomes Decidable

  • Stéphane Demri
  • Arnaud Sangnier
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6014)


We study the decidability status of model-checking freeze LTL over various subclasses of counter machines for which the reachability problem is known to be decidable (reversal-bounded counter machines, vector additions systems with states, flat counter machines, one-counter machines). In freeze LTL, a register can store a counter value and at some future position an equality test can be done between a register and a counter value. Herein, we complete an earlier work started on one-counter machines by considering other subclasses of counter machines, and especially the class of reversal-bounded counter machines. This gives us the opportuniy to provide a systematic classification that distinguishes determinism vs. nondeterminism and we consider subclasses of formulae by restricting the set of atomic formulae or/and the polarity of the occurrences of the freeze operators, leading to the flat fragment.


Model Check Temporal Logic Atomic Formula Hybrid Logic Reachability Problem 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Stéphane Demri
    • 1
  • Arnaud Sangnier
    • 2
  1. 1.LSVENS Cachan, CNRS, INRIA Saclay IdFFrance
  2. 2.Dipartimento di InformaticaUniversità di TorinoItaly

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