Describing behavior of processes with many-to-many interactions

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Processes are a key application area for formal models of concurrency. The core concepts of Petri nets have been adopted in research and industrial practice to describe and analyze the behavior of processes where each instance is executed in isolation. Unaddressed challenges arise when instances of processes may interact with each other in a one-to-many or many-to-many fashion. So far, behavioral models for describing such behavior either also include an explicit data model of the processes to describe many-to-many interactions, or cannot provide precise operational semantics. In this paper, we study the problem in detail through a fundamental example and evolve a few existing concepts from net theory towards many-to-many interactions. Specifically, we show that three concepts are required to provide an operational, true concurrency semantics to describe the behavior of processes with many-to-many interactions: unbounded dynamic synchronization of transitions, cardinality constraints limiting the size of the synchronization, and history-based correlation of token identities. The resulting formal model is orthogonal to all existing data modeling techniques, and thus allows to study the behavior of such processes in isolation, and to combine the model with existing and future data modeling techniques.

Original languageEnglish
Title of host publicationApplication and Theory of Petri Nets and Concurrency - 40th International Conference, PETRI NETS 2019, Proceedings
EditorsSusanna Donatelli, Stefan Haar
Number of pages22
ISBN (Print)9783030215705
Publication statusPublished - 1 Jan 2019
Event40th International Conference on Application and Theory of Petri Nets and Concurrency, (PetriNets2019) - Aachen, Germany
Duration: 23 Jun 201928 Jun 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11522 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference40th International Conference on Application and Theory of Petri Nets and Concurrency, (PetriNets2019)
Abbreviated titlePetriNets2019
Internet address


  • Many-to-many interactions
  • Modeling
  • Multi-instance processes
  • Petri nets
  • True-concurrency semantics


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