On reachability for hybrid automata over bounded time

Authors:
Thomas Brihaye;Laurent Doyen;Gilles Geeraerts;Joël Ouaknine;Jean-François Raskin;James Worrell
Affiliations:
Université de Mons, Belgium;LSV, ENS Cachan & CNRS, France;Université Libre de Bruxelles, Belgium;Oxford University Computing Laboratory, UK;Université Libre de Bruxelles, Belgium;Oxford University Computing Laboratory, UK
Venue:
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Year:
2011

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Abstract

This paper investigates the time-bounded version of the reachability problem for hybrid automata. This problem asks whether a given hybrid automaton can reach a given target location within T time units, where T is a constant rational value. We show that, in contrast to the classical (unbounded) reachability problem, the timed-bounded version is decidable for rectangular hybrid automata provided only non-negative rates are allowed. This class of systems is of practical interest and subsumes, among others, the class of stopwatch automata. We also show that the problem becomes undecidable if either diagonal constraints or both negative and positive rates are allowed.