TAILIEUCHUNG - CONCUR 2004 – Concurrency Theory- P17

CONCUR 2004 – Concurrency Theory- P17: The purpose of the CONCUR conferences is to bring together researchers, developers and students in order to advance the theory of concurrency and promote its applications. Interest in this topic is continually growing, as a consequence of the importance and ubiquity of concurrent systems and their applications, and of the scientific relevance of their foundations. | Open Maps Alternating Simulations and Control Synthesis PauloTabuada Department of Electrical Engineering University of Notre Dame Notre Dame IN 46556 ptabuada@ Abstract. Control synthesis is slowly transcending its traditional application domain within engineering to find interesting and useful applications in computer science. Synthesis of interfaces distributed network monitors or reactive programs are some examples that benefit from this design paradigm. In this paper we shed new light on the interplay between the fundamental notion of bisimulation and the control synthesis problem. We first revisit the notion of alternating simulation introduced by Alur and co-workers as it naturally captures important ingredients of the control synthesis problem. We then show that existence of controllers enforcing specifications through bisimulation alternating simulation or simulation can be characterized by the existence of certain alternating simulations and bisimulations between the specification and the system to be controlled. These results highlight and unify the role of simulations and bisimulations in the control synthesis setting for a wide range of concurrency models. This is achieved by developing our study within the framework of open maps. We illustrate our results on transition systems and timed transition systems. 1 Introduction Computer Science and Control Theory. The control synthesis problem is the central theme of control theory. The traditional setup consists of a system usually modeled by a differential equation with certain inputs that can be freely assigned and a specification. The objective is to synthesize a controller which based on the observation of the current system state changes the system inputs in order to alter its behavior and to enforce the specification. However many man made systems are not adequately described by differential equations and in the late 80 s Ramadage and Wonham initiated the application of control theoretic ideas .

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