The synthesis of controllers for discrete event systems, as introduced by Ramadge and Wonham, amounts to computing winning strategies in parity games. We show that in this framework it is possible to extend the specifications of the supervised systems as well as the constraints on the controllers by expressing them in the modal µ-calculus. In order to express unobservability constraints, we propose an extension of the modal µ-calculus in which one can specify whether an edge of a graph is a loop. This extended µ-calculus still has the interesting properties of the classical one. In particular it is equivalent to automata with loop testing. The problems such as emptiness testing and elimination of alternation are solvable for such automata. The method proposed in this paper to solve a control problem consists in transforming this problem into a problem of satisfiability of a µ-calculus formula so that the set of models of this formula is exactly the set of controllers that solve the problem. This transformation relies on a simple construction of the quotient of automata with loop testing by a deterministic transition system. This is enough to deal with centralized control problems. The solution of decentralized control problems uses a more involved construction of the quotient of two automata. This work extends the framework of Ramadge and Wonham in two directions. We consider infinite behaviours and arbitrary regular specifications, while the standard framework deals only with specifications on the set of finite paths of processes. We also allow dynamic changes of the set of observable and controllable events.

International audienceThis paper presents the BINCOA framework, whose goal is to ease the development of binary code analysers by providing an open formal model for low-level programs (typically: executable files), an XML format for easy exchange of models and some basic tool support. The BINCOA framework already comes with three different analysers, including simulation, test generation and Control-Flow Graph reconstruction

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In this paper, we present extensions of the framework of the µ-calculus which allow us to handle in a very generic and extensible way many control problems. The fundamental new tool is a division operator, and two new modalities are given as examples which allow us to handle observability and distinguishability. Furthermore, all this gives rise to a method for the synthesis of controllers which is implemented in a tool presented here.

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