Deriving Petri nets from finite transition systems

Abstract

This paper presents a novel method to derive a Petri Net from any specification model that can be mapped into a statebased representation with arcs labeled with symbols from an alphabet of events (a Transition System, TS). The method is based on the theory of regions for Elementary Transition Systems (ETS). Previous work has shown that, for any ETS, there exists a Petri Net with minimum transition count (one transition for each label) with a reachability graph isomorphic to the original Transition System. Our method extends and implements that theory by using the following three mechanisms that provide a framework for synthesis of safe Petri Nets from arbitrary TSs. First, the requirement of isomorphism is relaxed to bisimulation of TSs, thus extending the class of synthesizable TSs to a new class called Excitation-Closed Transition Systems (ECTS). Second, for the first time, we propose a method of PN synthesis for an arbitrary TS based on mapping a TS event into a set of transition labels in a PN. Third, the notion of irredundant region set is exploited, to minimize the number of places in the net without affecting its behavior. The synthesis method can derive different classes of place-irredundant Petri Nets (e.g., pure, free choice, unique choice) from the same TS, depending on the constraints imposed on the synthesis algorithm. This method has been implemented and applied in different frameworks. The results obtained from the experiments have demonstrated the wide applicability of the method.

Process Model Discovery: A Method Based on Transition System Decomposition

“…The state-based region approach was initially proposed by A. Ehrenfeucht and G. Rozenberg [16]. Later this approach was generalized by J. Cortadella et al [12,13]. An alternative generalization was proposed by J. Carmona et al [11].…”

“…State-based region algorithm First, we briefly describe the standard state-based region algorithm [12,13]. Let TS = (S, E, T, s in , S fin ) be a transition system and S ⊆ S be a subset of states.…”

“…Let us enumerate the properties of the standard state-based region algorithm [12,13], which will be used for the analysis of the discovery algorithm presented in this paper:…”

“…The standard state-based region algorithm [12,13] guarantees that there is a bisimilarity relation between the initial transition system and the reachability graph of the target Petri net. This property is inherited by a regular transition system under the assumption that a basic region algorithm will not produce reachability graphs with markings which dominate one another (m ⊆ m ).…”

Discovering Block-Structured Process Models from Incomplete Event Logs

“…For instance, after a transition system has been constructed from the log, state-based region miner techniques construct a Petri net by folding regions of states into places [4,28]. Typically, statebased region techniques provide rediscoverability guarantees [10], but have problems dealing with parallelism.…”