Minimum-time reachability in timed games

Authors:
Thomas Brihaye;Thomas A. Henzinger;Vinayak S. Prabhu;Jean-François Raskin
Affiliations:
LSV-CNRS & ENS de Cachan;Department of Computer and Communication Sciences, EPFL;Department of Electrical Engineering & Computer Sciences, UC Berkeley;Département d'Informatique, Université Libre de Bruxelles
Venue:
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Year:
2007

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Abstract

We consider the minimum-time reachability problem in concurrent two-player timed automaton game structures. We show how to compute the minimum time needed by a player to reach a target location against all possible choices of the opponent. We do not put any syntactic restriction on the game structure, nor do we require any player to guarantee time divergence. We only require players to use receptive strategies which do not block time. The minimal time is computed in part using a fixpoint expression, which we show can be evaluated on equivalence classes of a non-trivial extension of the clock-region equivalence relation for timed automata.