Unfolding Semantics of Petri Nets Based on Token Flows

Issue title: Petri Nets 2008

Article type: Research Article

Authors: Bergenthum, Robin | Mauser, Sebastian | Lorenz, Robert | Juhas, Gabriel

Affiliations: Department of Applied Computer Science, Catholic University of Eichstäatt-Ingolstadt, Germany. E-mail: {robin.bergenthum,sebastian.mauser}@ku-eichstaett.de | Department of Applied Computer Science, University of Augsburg, Germany. E-mail: robert.lorenz@informatik.uni-augsburg.de | Faculty of Electrical Engineering and Information Technology, Slovak University of Technology Bratislava, Slovak Republic. E-mail: gabriel.juhas@stuba.sk Abstract

Abstract: In this paper we propose two new unfolding semantics for general Petri nets combining the concept of prime event structures with the idea of token flows developed in [13]. In contrast to the standard unfolding based on branching processes, one of the presented unfolding models avoids to represent isomorphic processes while the other additionally reduces the number of (possibly nonisomorphic) processes with isomorphic underlying runs. We show that both the proposed unfolding models still represent the complete partial order behavior. Moreover, in both cases it is possible to construct complete finite prefixes for bounded nets through applying the known theory of cut-off events. In particular, canonical prefixes w.r.t. a given cutting context can be defined and computed for bounded nets. We present implementations of construction algorithms for complete finite prefixes of both the unfolding models. Experimental results show that the computed prefixes are much smaller and can be constructed significantly faster than in the case of the standard unfolding.

Keywords: Unfolding, Prime Event Structure, Canonical Prefix, Cutting Context, Petri Net

DOI: 10.3233/FI-2009-134

Journal: Fundamenta Informaticae, vol. 94, no. 3-4, pp. 331-360, 2009