Simultaneous Petri Net Synthesis

Abstract

Petri net synthesis deals with the problem whether, given a labelled transition system TS , one can find a Petri net N with an initial markingM0 such that the reachability graph of (N,M0) is isomorphic to TS . This may be preceded by a pre-synthesis phase that will quickly reject ill-formed transition systems (and give structural reasons for the failure) and otherwise build data structures needed by the proper synthesis. The last phase proceeds by solving systems of linear inequalities, and may still fail but for less transparent reasons. In this paper, we consider an extended problem. A finite set of transition systems {TS 1, . . . ,TSm} shall be called simultaneously Petri net solvable if there is a single Petri netN with several initial markings {M01, . . . ,M0m}, such that for every i = 1, . . . ,m, the reachability graph of (N,M0i) is isomorphic to TS i. The focus will be on choice-free nets, that is, nets without structural choices, and we explore how previously published efficient algorithms for the pre-synthesis and proper synthesis of bounded and choice-free Petri nets can be generalised for the simultaneous pre-synthesis and synthesis of such multi-marked nets. At the same time, the choice-free pre-synthesis of a single transition system shall be strengthened by introducing new structural checks.