Conference Paper

A generalized approach to supervisor synthesis

Inst. for Comput. Design & Fault Tolerance, Karlsruhe Univ., Germany
DOI: 10.1109/MEMCOD.2003.1210106 Conference: Formal Methods and Models for Co-Design, 2003. MEMOCODE '03. Proceedings. First ACM and IEEE International Conference on
Source: DBLP

ABSTRACT We present a generalization of the supervisory control problem proposed by Ramadge and Wonham. The objective of that problem is to synthesize a controller, which constrains a system's behavior according to a given specification, ensuring controllability and co-accessibility. By introducing a new representation of the solution using systems of μ-calculus equations we are able to handle these two conditions separately and thus to exchange the co-accessibility requirement by any μ-calculus expression. Well-known results on the complexity of μ-calculus model checking allow us to easily assess the computational complexity of any generalization. As an example we solve the synthesis problem under consideration of fairness constraints.

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    ABSTRACT: Verification procedures, which check whether a given system satisfies a given specification, are nowadays mature for industrial usage. The more general supervisor synthesis problem asks how a system has to be restricted or which actions have to be selected such that the system satisfies a given specification. Supervisor synthesis problems are often formulated in frameworks like game structures that are more general than the Kripke structures that are traditionally used in verification. For this reason, current verification tools can not be used for supervisory control problems. In this paper, however, we present a reduction of alternating time μ-calculus model checking problems (on game structures) to model checking problems of the μ-calculus on Kripke structures. As a result, arbitrary model checkers can be used to solve supervisor synthesis problems. As a demonstration of the applicability of our approach, we show how the classical supervisory control problems of Ramadge and Wonham can be solved within our framework.
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