Partial Order Semantics of Types of Nets

Authors:
Robert Lorenz;Gabriel Juhás;Sebastian Mauser
Affiliations:
Department of Computer Science, University of Augsburg, Germany;Faculty of Electrical Engineering and Information Technology, Slovak University of Technology, Bratislava, Slovakia;Department of Applied Computer Science, Catholic University of Eichstätt-Ingolstadt, Germany
Venue:
SOFSEM '09 Proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science
Year:
2009

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Abstract

In this paper we define partial order semantics of types of nets. Types of nets are a parametric definition of Petri nets originally developed for a general presentation of the synthesis of Petri nets from (step) transition systems. Partial order semantics of a concrete net (of a certain type) usually are given by the set of labelled partial orders (LPOs) enabled w.r.t. the net. For classical place/transition nets there are several equivalent characterizations of enabled LPOs. We discuss in which way the general notion of types of nets has to be restricted such that these characterizations can also be formulated for nets of such type. In particular we consider under which requirements enabled LPOs can be defined through token flows, which have been proven to be useful for efficient synthesis and verification of Petri nets. The presented concepts form the basis for a general presentation of the synthesis of Petri nets from sets of LPOs.