Lower and upper bounds in zone-based abstractions of timed automata

  • Authors:
  • Gerd Behrmann;Patricia Bouyer;Kim G. Larsen;Radek Pelánek

  • Affiliations:
  • BRICS, Aalborg University, Denmark;LSV, CNRS & ENS de Cachan, UMR, 8643, France;BRICS, Aalborg University, Denmark;Masaryk University Brno, 8643, Czech Republic

  • Venue:
  • International Journal on Software Tools for Technology Transfer (STTT)
  • Year:
  • 2006

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Abstract

Timed automata have an infinite semantics. For verification purposes, one usually uses zone-based abstractions w.r.t. the maximal constants to which clocks of the timed automaton are compared. We show that by distinguishing maximal lower and upper bounds, significantly coarser abstractions can be obtained. We show soundness and completeness of the new abstractions w.r.t. reachability and demonstrate how information about lower and upper bounds can be used to optimise the algorithm for bringing a difference bound matrix into normal form. Finally, we experimentally demonstrate that the new techniques dramatically increase the scalability of the real-time model checker UPPAAL.