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A Reachability Algorithm for General Petri Nets Based on Transition Invariants

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Mathematical Foundations of Computer Science 2006 (MFCS 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4162))

Abstract

A new reachability algorithm for general Petri nets is proposed. Given a Petri net with an initial and a target markings, a so called complemented Petri net is created first that consists of the given Petri net and an additional, complementary transition. Thereby, the reachability task is reduced to calculation and investigation of transition invariants (T-invariants) of the complemented Petri net. The algorithm finds all minimal-support T-invariants of the complemented Petri net and then calculates a finite set of linear combinations of minimal-support T-invariants, in which the complementary transition fires only once. Finally, for each T-invariant with a single firing of the complementary transition, the algorithm tries to create a reachability path from initial to target marking or determines that there is no such path.

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Author information

Authors and Affiliations

  1. Department of Computer Engineering, Eastern Mediterranean University, Magusa, KKTC, Mersin 10, Turkey

    Alexander E. Kostin

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  1. Alexander E. Kostin
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Editors and Affiliations

  1. Department of Computer Science, Comenius University, Mlynská dolina, 84248, Bratislava, Slovakia

    Rastislav Královič

  2. Institute of Informatics, University of Warsaw, Poland

    Paweł Urzyczyn

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Kostin, A.E. (2006). A Reachability Algorithm for General Petri Nets Based on Transition Invariants. In: Královič, R., Urzyczyn, P. (eds) Mathematical Foundations of Computer Science 2006. MFCS 2006. Lecture Notes in Computer Science, vol 4162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11821069_53

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  • DOI: https://doi.org/10.1007/11821069_53

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-37791-7

  • Online ISBN: 978-3-540-37793-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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