Affiliations: Faculty of Electrical Engineering and Information
Technology, Slovak University of Technology Bratislava, Slovakia.
gabriel.juhas@stuba.sk | Department of Applied Computer Science, Catholic
University of Eichstätt-Ingolstadt, Germany.
robert.lorenz@ku-eichstaett.de; sebastian.mauser@ku-eichstaett.de
Note: [] Address for correspondence: Department of Applied Computer
Science, Catholic University of Eichstätt-Ingolstadt, Germany
Abstract: In this paper, we show how to obtain causal semantics distinguishing
"earlier than" and "not later than" causality between events from algebraic
semantics of Petri nets. Janicki and Koutny introduced so called stratified order structures
(so-structures) to describe such causal semantics. To obtain algebraic
semantics, we redefine our own algebraic approach generating rewrite terms via
partial operations of synchronous composition, concurrent composition and
sequential composition. These terms are used to produce so-structures which
define causal behavior consistent with the (operational) step semantics. For
concrete Petri net classes with causal semantics derived from processes minimal
so-structures obtained from rewrite terms coincide with minimal so-structures
given by processes. This is demonstrated for elementary nets with inhibitor
arcs.
Keywords: theory of concurrency, algebraic Petri nets, causal semantics, process terms, inhibitor arcs, synchronicity
