Synthesis of Petri nets from infinite partial languages

In this paper we present an algorithm to synthesize a finite unlabeled place/transition Petri net (p/t-net) from a possibly infinite partial language, which is given by a term over a finite set of labeled partial orders using operators for union, iteration, parallel composition and sequential composition. The synthesis algorithm is based on the theory of regions for partial languages presented in [18] and produces a p/t-net having minimal net behavior including the given partial language. The algorithm uses linear programming techniques that were already successfully applied in [17] for the synthesis of p/t-nets from finite partial languages.