From Behaviour to Nets via Regions

Koutny, M; Mikulski, L; Pietkiewicz-Koutny, M

doi:10.1007/978-3-662-73305-9_4

From Behaviour to Nets via Regions

Lookup NU author(s): Emeritus Professor Maciej Koutny ORCiD, Dr Lukasz Mikulski, Dr Marta Koutny ORCiD

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Abstract

© The Author(s), under exclusive license to Springer-Verlag GmbH, DE, part of Springer Nature 2026. The behaviour of concurrent systems is often given in the form of graphs/transition systems that show the execution of systems’ actions (or transitions). The extraction of the systems’ topology from the transition systems’ specification—with every transition and its environment (places) clearly identified—is possible by synthesising Petri net models from given transition systems. A particularly successful technique is based on the notion of a region of a transition system, where each region is used to define a place in the synthesised Petri net. The class of Elementary Net systems is a fundamental Petri net model with markings that can be represented by sets of the marked places. Their standard semantics is based on sequences of executed transitions, which can be understood as (labelled) total orders. In this paper, and in its workshop precursor [32], we consider a newly proposed semantics based on (labelled) interval (partial) orders which allows one to describe behaviours where transitions have non-atomic duration. For such a semantical model, we consider the net synthesis problem, and show that the standard notion of a region of a transition system can still be applied.