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Algorithms for computing a minimally restrictive control in the context of supervisory control of discrete event systems have been well developed when both the plant and the desired behavior are given as regular languages. In this paper we extend such prior results by presenting an algorithm for computing a minimally restrictive control when the plant behavior is a deterministic Petri net language and the desired behavior is a regular language. As part of the development of the algorithm, we establish the following results that are of independent interest: (i) The problem of determining whether a given deterministic Petri net language is controllable with respect to another deterministic Petri net language is reducible to a reachability problem of Petri nets. (ii) The problem of synthesizing the minimally restrictive supervisor so that the controlled system generates the supremal controllable sublanguage is reducible to a forbidden marking problem. In particular, we can directly identify the set of forbidden markings without having to construct any reachability tree.

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