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Petri Nets: A Simple Language and Tool for Modeling Complex Ideas

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Carl Adam Petri: Ideas, Personality, Impact

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Abstract

For almost 40 years Petri nets and also many of Petri’s other ideas provided the author with motivation and a convenient tool for his research related to concurrency.

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Notes

  1. 1.

    A partial order <  (of events) on X is an interval order if and only if there are mappings B: X → Y, E: X → Y , some Y  and a total order ≺ (of event beginning and endings) on Y  such that B(x) ≺ E(x) and \(x < y \Leftrightarrow E\left ( x \right ) \prec B(y)\), for all x, y ∈ X (cf. [2, 5]). Often Bx and Ex are written instead of B(x) and E(x). In Fig. 2, the total order ≺io is a possible total order representation of the interval order <io.

References

  1. T. Agerwala, M. Flynn, Comments on capabilities, limitations and “correctness” of Petri nets. Comput. Architect. News 4(2), 81–86 (1973)

    Article  Google Scholar 

  2. P.C. Fishburn, Intransitive indifference with unequal indifference intervals. J. Math. Psychol. 7, 144–149 (1970)

    Article  MathSciNet  Google Scholar 

  3. R. Janicki, Synthesis of concurrent schemes, in Proceedings of MFCS’78, ed. by J. Winkowski. Lecture Notes in Computer Science, vol. 64 (Springer, Berlin, 1978), pp. 298–307

    Chapter  Google Scholar 

  4. R. Janicki, M. Koutny, Using optimal simulations to reduce reachability graphs, in Proceedings of CAV’90, ed. by E.M. Clarke, R.P. Kurshan. Lecture Notes in Computer Science, vol. 531 (Springer, Berlin, 1991), pp. 166–175

    Google Scholar 

  5. R. Janicki, M. Koutny, Structure of concurrency. Theor. Comput. Sci. 112(1), 5–52 (1993)

    Article  MathSciNet  Google Scholar 

  6. R. Janicki, X. Yin, Modeling concurrency with interval traces. Inf. Comput. 25(1), 78–108 (2017)

    Article  MathSciNet  Google Scholar 

  7. R. Janicki, J. Kleijn, M. Koutny, Ł. Mikulski, Step traces. Acta Inf. 53, 35–65 (2016)

    Article  MathSciNet  Google Scholar 

  8. J. Kleijn, M. Koutny, Mutex causality in processes and traces of general elementary nets. Fundam. Inf. 122(1,2), 119–146 (2013)

    Google Scholar 

  9. A. Mazurkiewicz, Concurrent program schemes and their interpretation. TR DAIMIPB-78, Computer Science Department, Aarhus University (1977)

    Google Scholar 

  10. C.A. Petri, Concepts of net theory, in Proceedings of MFCS’73, Štrbské Pleso (1973), pp. 137–146

    Google Scholar 

  11. C.A. Petri, Nets, time and space. Theor. Comput. Sci. 153(1–2), 3–48 (1996)

    Article  MathSciNet  Google Scholar 

  12. R.J. Van Glabbeek, F. Vaandrager, Petri net models for algebraic theories of concurrency, in PARLE Vol. II, ed. by J.W. de Bakker et al. Lecture Notes in Computer Science, vol. 259 (Springer, Berlin, 1987), pp. 224–242

    Google Scholar 

  13. W. Vogler, Partial order semantics and read arcs. Theor. Comput. Sci. 286(1), 3363 (2002)

    Article  MathSciNet  Google Scholar 

  14. N. Wiener, A contribution to the theory of relative position. Proc. Camb. Philos. Soc. 17(5), 441–449 (1914)

    MATH  Google Scholar 

  15. W.M. Zuberek, Timed Petri nets and preliminary performance evaluation, in Proceedings of the 7th Annual Symposium on Computer Architecture (ACM, New York, 1980), pp. 89–96

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computing and Software, McMaster University, Hamilton, ON, Canada

    Ryszard Janicki

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  1. Ryszard Janicki
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Correspondence to Ryszard Janicki .

Editor information

Editors and Affiliations

  1. Institut für Informatik, Humboldt-Universität zu Berlin, Berlin, Germany

    Wolfgang Reisig

  2. Leiden Institute of Advanced Computer Science, Leiden University, Leiden, The Netherlands

    Grzegorz Rozenberg

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Janicki, R. (2019). Petri Nets: A Simple Language and Tool for Modeling Complex Ideas. In: Reisig, W., Rozenberg, G. (eds) Carl Adam Petri: Ideas, Personality, Impact. Springer, Cham. https://doi.org/10.1007/978-3-319-96154-5_9

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  • DOI: https://doi.org/10.1007/978-3-319-96154-5_9

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-96154-5

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