Skip to main content
SpringerLink
Log in

Deterministic Concurrent Systems

  • Conference paper
  • First Online:
Application and Theory of Petri Nets and Concurrency (PETRI NETS 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12734))

  • 562 Accesses

Abstract

Deterministic concurrent system are “locally commutative” concurrent systems. We characterise these systems by means of their combinatorial properties.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    In the literature, trace monoids are also called free partially commutative monoids, and they also correspond to right-angled Artin-Tits monoids.

  2. 2.

    Recall that, if \(c\le u\) with \(c,u\in {\mathcal {M}}\), we denote by \(c\backslash u\) the left cancellation of u by c, which is the unique trace \(v\in {\mathcal {M}}\) such that \(c\cdot v=u\).

  3. 3.

    This actually holds for any concurrent system, not necessarily deterministic, if \(c_\alpha \) is taken to be any maximal element in \(\mathscr {C}_\alpha \).

References

  1. Abbes, S.: Markovian dynamics of concurrent systems. Discrete Event Dyn. Syst. 29(4), 527–566 (2019). https://doi.org/10.1007/s10626-019-00291-z

    Article  MathSciNet  MATH  Google Scholar 

  2. Abbes, S., Mairesse, J.: Uniform and Bernoulli measures on the boundary of trace monoids. J. Comb. Theor. Ser. A 135, 201–236 (2015)

    Article  MathSciNet  Google Scholar 

  3. Abbes, S., Mairesse, J., Chen, Y.-T.: A spectral property for concurrent systems and some probabilistic applications. Submitted for publication. Available at https://arxiv.org/abs/2003.03762 (2020)

    Google Scholar 

  4. Cartier, P., Foata, D.: Problèmes combinatoires de commutation et réarrangements. LNM, vol. 85. Springer, Heidelberg (1969). https://doi.org/10.1007/BFb0079468

    Book  MATH  Google Scholar 

  5. Dehornoy, P., Digne, F., Godelle, E., Krammer, D., Michel, J.: Foundations of Garside Theory. EMS (2015)

    Google Scholar 

  6. Diekert, V.: Combinatorics on Traces. LNCS, vol. 454. Springer, Heidelberg (1990). https://doi.org/10.1007/3-540-53031-2

    Book  MATH  Google Scholar 

  7. Diekert, V., Rozenberg, G. (eds.): The Book of Traces. World Scientific (1995)

    Google Scholar 

  8. Goldwurm, M., Santini, M.: Clique polynomials have a unique root of smallest modulus. Inform. Process. Lett. 75(3), 127–132 (2000)

    Article  MathSciNet  Google Scholar 

  9. Krob, D., Mairesse, J., Michos, I.: Computing the average parallelism in trace monoids. Discrete Math. 273, 131–162 (2003)

    Article  MathSciNet  Google Scholar 

  10. Nielsen, M., Plotkin, G., Winskel, G.: Petri nets, event structures and domains, part I. Theor. Comput. Sci. 13, 85–108 (1981)

    Article  Google Scholar 

  11. Reisig, W.: Petri Nets- An Introduction. Springer, Heidelberg (1985). https://doi.org/10.1007/978-3-642-69968-9

    Book  MATH  Google Scholar 

  12. Rota, G.-C.: On the foundations of combinatorial theory I. Theory of Möbius functions. Z. Wahrscheinlichkeitstheorie 2, 340–368 (1964). https://doi.org/10.1007/BF00531932

    Article  MATH  Google Scholar 

  13. Viennot, G.X.: Heaps of pieces, I: Basic definitions and combinatorial lemmas. In: Labelle, G., Leroux, P. (eds.) Combinatoire énumérative. LNM, vol. 1234, pp. 321–350. Springer, Heidelberg (1986). https://doi.org/10.1007/BFb0072524

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Université de Paris - IRIF (CNRS UMR 8243), Paris, France

    Samy Abbes

Authors
  1. Samy Abbes
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Samy Abbes .

Editor information

Editors and Affiliations

  1. Université de Genève, Carouge, Switzerland

    Didier Buchs

  2. Universitat Politècnica de Catalunya, Barcelona, Spain

    Josep Carmona

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Abbes, S. (2021). Deterministic Concurrent Systems. In: Buchs, D., Carmona, J. (eds) Application and Theory of Petri Nets and Concurrency. PETRI NETS 2021. Lecture Notes in Computer Science(), vol 12734. Springer, Cham. https://doi.org/10.1007/978-3-030-76983-3_21

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-76983-3_21

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-76982-6

  • Online ISBN: 978-3-030-76983-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation