Computing Accumulated Delays in Real-time Systems

  • Authors:
  • Rajeev Alur;Costas Courcoubetis;Thomas A. Henzinger

  • Affiliations:
  • Bell Laboratories, Murray Hill, New Jersey, U.S.A. E-mail: alur@research.bell-labs.com;Department of Computer Science, University of Crete, and Institute of Computer Science, FORTH, Heraklion, Greece. E-mail: courcou@ics.forth.gr;Department of Electrical Engineering and Computer Science, University of California at Berkeley, U.S.A. E-mail: tah@eecs.berkeley.edu

  • Venue:
  • Formal Methods in System Design - Special issue on computer aided verification (CAV 93)
  • Year:
  • 1997

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Abstract

We present a verification algorithm for duration properties ofreal-time systems. While simple real-time properties constrain thetotal elapsed time between events, duration properties constrain theaccumulated satisfaction time of state predicates. We formalize theconcept of durations by introducing duration measures for timedautomata. A duration measure assigns to each finite run of a timedautomaton a real number —the duration ofthe run— which may be the accumulated satisfaction time of astate predicate along the run. Given a timed automaton with aduration measure, an initial and a final state, and an arithmeticconstraint, the duration-bounded reachability problem asks if there is a run of the automaton from theinitial state to the final state such that the duration of the runsatisfies the constraint. Our main result is an (optimal) PSPACE decision procedure for the duration-bounded reachability problem.