Skip to main content
SpringerLink
Log in

Recognizable and rational languages of finite and infinite traces

  • Trace Theory
  • Conference paper
  • First Online:
Book cover STACS 91 (STACS 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 480))

Included in the following conference series:

Abstract

Trace languages are used in computer science to provide a description of the behaviours of concurrent systems. If we are interested in systems which never stop then we have to consider languages of infinite traces. In this paper, we introduce and study recognizable and rational languages of finite and infinite traces. We characterize recognizable languages by means of a syntactic congruence. We prove that the family of recognizable languages is strictly included in the family of rational languages. Next, we study the closure properties of the family of recognizable languages. We prove that this family is closed under the Boolean operations and under concatenation. Contrary to the (finite) iteration, the infinite iteration of a finite trace is proved to be recognizable. We conclude this paper with some open problems.

This work has been supported by the ESPRIT Basic Research Action No. 3166: Algebraic and Syntactic Methods in Computer Science (ASMICS) and by the PRC Math-Info.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

5. References

  1. A. ARNOLD, “A syntactic congruence for rational ω-languages”, Theoretical Computer Science 39, p. 333–335, 1985.

    Article  Google Scholar 

  2. I.J. AALBERSBERG and G. ROZENBERG, “Theory of traces”, Theoretical Computer Science 60, p. 1–82, 1988.

    Article  Google Scholar 

  3. J.R. BUCHI, “On a decision method in restricted second order arithmetic”, Proc. Internat. Congress on Logic, Methodology and Philosophy (Standford University Press), p. 1–11, 1962.

    Google Scholar 

  4. P. CARTIER and D. FOATA, “Problèmes combinatoires de commutation et réarrangements”, Lecture Notes in Math. 85, 1969.

    Google Scholar 

  5. R. CORI and Y. METIVIER, “Recognizable subsets of some partially abelian monoids”, Theoretical Computer Science 35, p. 179–189, 1985.

    Article  Google Scholar 

  6. R. CORI and D. PERRIN, “Automates et commutations partielles”, RAIRO Theoretical Informatics and Applications 19, p. 21–32, 1985.

    Google Scholar 

  7. V. DIEKERT, “Combinatorics on Traces”, Lecture Notes in Computer Science 454, 1990.

    Google Scholar 

  8. S. EILENBERG, “Automata, Languages and Machines”, Academic Press, New York, 1974.

    Google Scholar 

  9. M. FLIESS, “Matrices de Hankel”, J. Math. pures et appl. 53, p. 197–224, 1974.

    Google Scholar 

  10. M.P. FLE and G. ROUCAIROL, “Maximal serializability of iterated transactions”, Theoretical Computer Science 38, p. 1–16, 1985.

    Article  Google Scholar 

  11. P. GASTIN, “Un modèle asynchrone pour les systèmes distribués”, Theoretical Computer Science 74, p. 121–162, 1990.

    Article  Google Scholar 

  12. P. GASTIN, “Infinite traces”, Proceedings of the Spring School of Theoretical Computer Science on “Semantics of concurrency”, Lecture Notes in Computer Science 469, 1990.

    Google Scholar 

  13. R. L. GRAHAM, “Rudiments of Ramsey theory”, Regional conference series in mathematics 45, 1981.

    Google Scholar 

  14. P. GASTIN and B. ROZOY, “The Poset of infinitary traces”, Tech. Rep. 90-24, LITP, Université Paris 6, France, 1990.

    Google Scholar 

  15. H.J. HOOGEBOOM and G. ROZENBERG, “Infinitary languages: basic theory and applications to concurrent systems”, Lecture Notes in Computer Science 224, p. 266–342, 1986.

    Google Scholar 

  16. M.Z. KWIATKOWSKA, “On infinitary trace languages”, Tech. Rep. 31, University of Leicester, England, 1989.

    Google Scholar 

  17. M. LOTHAIRE, “Combinatorics on words”, Addison Wesley, 1983.

    Google Scholar 

  18. A. MAZURKIEWICZ, “Trace theory”, Advanced Course on Petri Nets, Lecture Notes in Computer Science 255, p. 279–324, 1986.

    Google Scholar 

  19. Y. METIVIER, “Une condition suffisante de reconnaissabilité dans un monoïde partiellement commutatif”, RAIRO Theoretical Informatics and Applications 20, p. 121–127, 1986.

    Google Scholar 

  20. Y. METIVIER, “On recognizable subsets in free partially commutative monoids”, ICALP 1986, Lecture Notes in Computer Science 226, p. 254–264, 1986.

    Google Scholar 

  21. D.E. MULLER, “Infinite sequences and finite machines”, Proc. 4th IEEE Ann. Symp. on Switching Circuit Theory and Logical Design, p. 3–16, 1963.

    Google Scholar 

  22. E. OCHMANSKI, “Regular behaviour of concurrent systems”, Bulletin of EATCS 27, p. 56–67, October 1985.

    Google Scholar 

  23. D. PERRIN, “Partial commutations”, ICALP 89, Lecture Notes in Computer Science 372, p. 637–651, 1989.

    Google Scholar 

  24. D.PERRIN and J.E. PIN, “Mots Infinis”, Tech. Rep., LITP, Université Paris 6, France, 1990. Book to appear.

    Google Scholar 

  25. B. ROZOY, “On Traces, Partial Order Sets and Recognizability”, ISCIS V, Cappadocia, Turkey, proceedings to appear, 1990.

    Google Scholar 

  26. J. SAKAROVITCH, “On regular trace languages”, Theoretical Computer Science 52, p. 59–75, 1987.

    Article  Google Scholar 

  27. W. THOMAS, “Automata on infinite objects”, to appear in Handbook of Theoretical Computer Science (J.V. Leeuwen, Ed.), North-Holland, Amsterdam.

    Google Scholar 

  28. W. THOMAS, “On logical definability of trace languages”, Proceedings of the ASMICS Workshop on Partially Commutative Monoids, Tech. Rep. TUM-I 9002, Technische Universität München, 1989.

    Google Scholar 

  29. W. ZIELONKA, “Notes on finite asynchronous automata and trace languages”, RAIRO Theoretical Informatics and Applications 21, p. 99–135, 1987.

    Google Scholar 

  30. W. ZIELONKA, “Safe execution of recognizable trace Languages by asynchronous automata”, Lecture Notes in Computer Science 363, p. 278–289, 1989.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Université Paris 6 LITP, 4, Place Jussieu, 75252, Paris Cedex 05, France

    Paul Gastin

Authors
  1. Paul Gastin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Christian Choffrut Matthias Jantzen

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gastin, P. (1991). Recognizable and rational languages of finite and infinite traces. In: Choffrut, C., Jantzen, M. (eds) STACS 91. STACS 1991. Lecture Notes in Computer Science, vol 480. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0020790

Download citation

  • DOI: https://doi.org/10.1007/BFb0020790

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53709-0

  • Online ISBN: 978-3-540-47002-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation