In this paper, we propose a first efficient on-the-fly algorithm for solving games based on timed game automata with respect to reachability and safety properties. The algorithm we propose is a symbolic extension of the on-the-fly algorithm suggested by Liu & Smolka for linear-time model-checking of finite-state systems. Being on-the-fly, the symbolic algorithm may terminate long before having explored the entire state-space. Also the individual steps of the algorithm are carried out efficiently by the use of so-called zones as the underlying data structure. Various optimizations of the basic symbolic algorithm are proposed as well as methods for obtaining time-optimal winning strategies (for reachability games). Extensive evaluation of an experimental implementation of the algorithm yields very encouraging performance results.
Joint work with Franck Cassez, Alexandre David, Kim G. Larsen, and Didier Lime.
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