Skip to main content

Modelling Concurrency with Quotient Monoids

  • Conference paper
Applications and Theory of Petri Nets (PETRI NETS 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5062))

Included in the following conference series:

Abstract

Four quotient monoids over step sequences and one with compound generators are introduced and discussed. They all can be regarded as extensions (of various degrees) of Mazurkiewicz traces [14] and comtraces of [10].

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Cartier, P., Foata, D.: Problèmes combinatoires de commutation et ré-arrangements. Lecture Notes in Mathematics, vol. 85. Springer, Heidelberg (1969)

    Google Scholar 

  2. Cohn, P.M., Reidel, D.: Universal Algebra (1981)

    Google Scholar 

  3. Davillers, R., Janicki, R., Koutny, M., Lauer, P.E.: Concurrent and Maximally Concurrent Evolution of Non-sequential Systems. Theoretical Computer Science 43, 213–238 (1986)

    Article  MathSciNet  Google Scholar 

  4. Desel, J.: Private Information, Communicated to the authors by G. Juhás (2007)

    Google Scholar 

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

    Google Scholar 

  6. Gaifman, H., Pratt, V.: Partial Order Models of Concurrency and the Computation of Function. In: Proc. of LICS 1987, pp. 72–85. IEEE, Los Alamitos (1987)

    Google Scholar 

  7. Guo, G., Janicki, R.: Modelling Concurrent Behaviours by Commutativity and Weak Causality Relations. In: Kirchner, H., Ringeissen, C. (eds.) AMAST 2002. LNCS, vol. 2422, pp. 178–191. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  8. Janicki, R., Koutny, M.: Invariants and Paradigms of Concurrency Theory. In: Aarts, E.H.L., van Leeuwen, J., Rem, M. (eds.) PARLE 1991. LNCS, vol. 506, pp. 59–74. Springer, Heidelberg (1991)

    Google Scholar 

  9. Janicki, R., Koutny, M.: Structure of Concurrency. Theoretical Compututer Science 112(1), 5–52 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  10. Janicki, R., Koutny, M.: Semantics of Inhibitor Nets. Information and Computation 123(1), 1–16 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  11. Janicki, R., Koutny, M.: Fundamentals of Modelling Concurrency Using Discrete Relational Structures. Acta Informatica 34, 367–388 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  12. Juhás, G., Lorenz, R., Mauser, S.: Synchronous + Concurrent + Sequential = Earlier Than + Not Later Than. In: Proc. of ACSD 2006 (Application of Concurrency to System Design), Turku, Finland, pp. 261–272. IEEE Press, Los Alamitos (2006)

    Google Scholar 

  13. Kleijn, H.C.M., Koutny, M.: Process Semantics of General Inhibitor Nets. Information and Computation 190, 18–69 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  14. Mazurkiewicz, A.: Introduction to Trace Theory, in [5], pp. 3–42

    Google Scholar 

  15. Ochmański, E.: Recognizable Trace Languages, in [5], pp. 167–204

    Google Scholar 

  16. Shields, M.W.: Adequate Path Expressions. In: Kahn, G. (ed.) Semantics of Concurrent Computation. LNCS, vol. 70, pp. 249–265. Springer, Heidelberg (1979)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Kees M. van Hee Rüdiger Valk

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Janicki, R., Lê, D.T.M. (2008). Modelling Concurrency with Quotient Monoids. In: van Hee, K.M., Valk, R. (eds) Applications and Theory of Petri Nets. PETRI NETS 2008. Lecture Notes in Computer Science, vol 5062. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68746-7_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-68746-7_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-68745-0

  • Online ISBN: 978-3-540-68746-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics