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 1. The algorithm we propose is a symbolic extension of the on-the-fly algorithm suggested by Liu & Smolka [15] 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. 1 Though timed games for long have been known to be decidable there has until now been a lack of efficient and truly on-the-fly algorithms for their analysis.

Abstract. In 2005 we proposed the first efficient on-the-fly algorithm for solving games based on timed game automata with respect to reachability and safety properties. The first prototype presented at that time has now matured to a fully integrated tool with dramatic improvements both in terms of performance and the availability of the extended input language of Uppaal-4.0. The new tool can output strategies or let the user play against them both from the command line and from the graphical simulator that was completely re-designed.