Symbolic Controller Synthesis for Discrete and Timed Systems

This paper presents algorithms for the symbolic synthesis of discrete and real-time controllers. At the semantic level the controller is synthesized by finding a winning strategy for certain games defined by automata or by timed-automata. The algorithms for finding such strategies need, this way or another, to search the state-space of the system which grows exponentially with the number of components. Symbolic methods allow such a search to be conducted without necessarily enumerating the state-space. This is achieved by representing sets of states using formulae (syntactic objects) over state variables. Although in the worst case such methods are as bad as enumerative ones, many huge practical problems can be treated by fine-tuned symbolic methods. In this paper the scope of these methods is extended from analysis to synthesis and from purely discrete systems to real-time systems.

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