Efficient On-the-Fly Algorithms for the Analysis of Timed Games

Abstract

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.

Combining Symbolic Representations for Solving Timed Games

“…Based on a prototype that combines binary decision diagrams [7,9] and difference bound matrices [5], we experimentally evaluate the technique on standard benchmarks from timed controller synthesis. The results clearly demonstrate the potential of the new approach concerning running time and memory consumption compared to the classical on-the-fly algorithm implemented in Uppaal-Tiga [10,4]. …”

“…The automated analysis of such so-called open systems requires a game-based computational model where an internal controller plays against an external environment. Solving problems defined on open systems (such as, e.g., timed controller synthesis [15]) is an active area of research [15,3,13,1,10,4,8,16] and usually corresponds to computing winning strategies in two-player games played on timed automata.…”

“…Current timed game solvers such as Uppaal-Tiga [10,4] represent the continuous parts symbolically, but the location information explicitly. Hence, such semi-symbolic representations fail in the analysis of timed systems with many concurrent components causing a discrete blow-up in the state space.…”

“…We obtain the abstractions by merging locations such that the abstract control structure strictly weakens one player and strengthens her opponent. For each abstraction, we apply traditional solving algorithms to obtain an under-and an over-approximation of the winning states of the reachability player (e.g., one can use [10], which works fine for timed games with few locations, to obtain under-approximations).…”

The role of supervisory controller synthesis in automatic control software development

“…This makes the latter technique more general and the main research seems to focus on decidability results, mainly relying on game-theoretic approaches. Some of the results are applicable in the systems engineering domain, e.g., synthesis of time-optimal schedulers [20]. However, for the most part, the application of these two techniques differs considerably, as the supervisory control community focuses on techniques and approaches viable for solving industriallyrelevant problems, often having to compromise between expressivity and efficiency.…”