Dynamical Properties of Timed Automata

  • Authors:

  • Anuj Puri

  • Affiliations:

  • University of California, 195 M Cory Hall, Berkeley, CA 94720

  • Venue:
  • Discrete Event Dynamic Systems
  • Year:
  • 2000

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Abstract

Timed automata are an important model forspecifying and analyzing real-time systems. The main analysisperformed on timed automata is the reachability analysis. Inthis paper we show that the standard approach for performingreachability analysis is not correct when the clocks drift evenby a very small amount. Our formulation of the reachability problemfor timed automata is as follows: we define the set R^*(T,Z_0)=\cap_{\eps0}\reach(T_\eps,Z_0)where T_\eps is obtained from timed automaton Tby allowing an \eps drift in the clocks. R^*(T,Z_0)is the set of states which can be reached in the timed automatonT from the initial states in Z_0 whenthe clocks drift by an infinitesimally small amount. We presentan algorithm for computing R^*(T,Z_0) and providea proof of its correctness. We show that R^*(T,Z_0)is robust with respect to various types of modeling errors. Toprove the correctness of our algorithm, we need to understandthe dynamics of timed automata—in particular, the structureof the limit cycles of timed automata.