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,
sebastian.mauser}@ku-eichstaett.de
Note: [] Address for correspondence: Faculty of Electrical Engineering
and Information Technology, Slovak University of Technology, Bratislava,
Slovakia
Abstract: In the first part of this paper we extend the semantical framework
proposed in [22] for process and causality semantics of Petri nets by an
additional aim, firstly mentioned in the habilitation thesis [15]. The aim
states that causality semantics deduced from process nets should be complete
w.r.t. step semantics of a Petri net in the sense that each causality structure
which is enabled w.r.t. step semantics corresponds to some process net. In the second part of this paper we examine several process
semantics of different Petri net classes w.r.t. this aim. While it is well
known that it is satisfied by the process semantics of place/transition Petri
nets (p/t-nets), we show in particular that the process semantics of p/t-nets
with weighted inhibitor arcs (PTI-nets) proposed in [22] does not satisfy the
aim. We develop a modified process semantics of PTI-nets fulfilling the aim of
completeness and also all remaining axioms of the semantical framework.
Finally, we sketch results in literature concerning the aim of completeness for
process definitions of various further Petri net classes. The paper is a revised and extended version of the conference paper
[18].
Keywords: Petri Net, Inhibitor Net, Process Semantics, Causal Semantics, Completeness
