Process Description Languages and Methods: Introduction to the Chapter Petri Nets and Related Approaches in Engineering

Coupling of interorganizational business processes in electronic markets is a difficult and time-consuming task. In practice, business processes are geographically distributed, which makes it particularly difficult for business partners to coordinate their supply chains and customer relationship management with business units. By using formal description languages such as Petri Nets for modeling interorganizational business processes, purely syntactic composition problems of distributed business environments can be solved. However, the missing semantic representation of Petri Nets can hamper the interconnectivity of business processes. Usually, several business partners, even if they share similar demands, have their own specific vocabularies. By representing business processes with Petri Nets in combination with the Web ontology language (OWL), our approach provides flexibility, ease of integration, and a significant level of automation of loosely coupled business processes even if they do not share their respective vocabularies.

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Behavioural Equivalence for Infinite Systems—Partially Decidable!

BRICS Report Series ◽

10.7146/brics.v2i55.19956 ◽

1995 ◽

Vol 2 (55) ◽

Cited By ~ 1

Author(s):

Mogens Nielsen ◽

Kim Sunesen

Keyword(s):

Petri Nets ◽

Parallel Processes ◽

Significant Difference ◽

Finite State ◽

Infinite State Systems ◽

Description Languages ◽

Traditional Approaches ◽

Language Equivalence ◽

Infinite State

For finite-state systems non-interleaving equivalences are computationally at least as hard as interleaving equivalences. In this paper we show that when moving to infinite-state systems, this situation may change dramatically. We compare standard language equivalence for process description languages with two generalizations based on traditional approaches capturing non-interleaving behaviour, pomsets representing global causal dependency, and locality representing spatial distribution of events. We first study equivalences on Basic Parallel Processes, BPP, a process calculus equivalent to communication free Petri nets. For this simple process language our two notions of non-interleaving equivalences agree. More interestingly, we show that they are decidable, contrasting a result of Hirshfeld that standard interleaving language equivalence is undecidable. Our result is inspired by a recent result of Esparza and Kiehn, showing the same phenomenon in the setting of model checking. We follow up investigating to which extent the result extends to larger subsets of CCS and TCSP. We discover a significant difference between our non-interleaving equivalences. We show that for a certain non-trivial subclass of processes between BPP and TCSP, not only are the two equivalences different, but one (locality) is decidable whereas the other (pomsets) is not. The decidability result for locality is proved by a reduction to the reachability problem for Petri nets.

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