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On the star operation and the finite power property in free partially commutative monoids

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STACS 94 (STACS 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 775))

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Abstract

We prove that if it is decidable whether X * is recognizable for a recognizable subset X of a free partially commutative monoid, then it is decidable whether a recognizable subset of a free partially commutative monoid possesses the finite power property. We prove that if every trace of a set X is connected, we can decide whether X possesses the finite power property. Finally, it is also shown that if X is a finite set containing at most four traces, it is decidable whether X * is recognizable.

This work has been supported by Esprit Basic Research Actions ASMICS II.

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References

  1. P. Cartier and D. Foata, Problèmes combinatoires de commutation et réarrangements, Lecture Notes in Math. 85, 1969.

    Google Scholar 

  2. R. Cori and Y. Métivier, Recognizable subsets of some partially abelian monoids, Theoret. Comput. Sci. 35, p179–189, 1985.

    Google Scholar 

  3. R. Cori and D. Perrin, Automates et commutations partielles, Sur la reconnaissabilité dans les monoÏdes partiellement comutatif libres, RAIRO, Theoretical Informatics and Applications 19, p 21–32, 1985.

    Google Scholar 

  4. C. Duboc, On some equations in free partially commutative monoids, Theoret. Comput. Sci. 46, p159–174, 1986.

    Google Scholar 

  5. S. Eilenberg, Automata, Languages and Machines, Academic Press, New York, 1974.

    Google Scholar 

  6. M. Fliess, Matrices de Hankel, J. Math Pures et Appl. 53, p197–224, 1974.

    Google Scholar 

  7. M.P. Flé and G. Roucairol, Maximal seriazibility of iterated transactions, Theoret. Comput. Sci. 38, p1–16, 1985.

    Google Scholar 

  8. P. Gastin, E. Ochmański, A. Petit, B. Rozoy, Decidability of the Star Problem in A*× {b}*, Inform. Process. Lett. 44, p65–71, 1992.

    Google Scholar 

  9. S. Ginsburg and E. Spanier, Semigroups, presburger formulas and languages, Pacific journal of mathematics 16, p285–296, 1966.

    Google Scholar 

  10. S. Ginsburg and E. Spanier, Bounded regular sets, Proceedings of the AMS, vol. 17(5), p1043–1049, 1966.

    Google Scholar 

  11. K. Hashigushi, A decision procedure for the order of regular events, Theoret. Comput. Sci. 8, p69–72, 1979.

    Google Scholar 

  12. K. Hashigushi, Limitedness Theorem on Finite Automata with Distance Functions, J. of Computer and System Science24, p233–244, 1982.

    Google Scholar 

  13. K. Hashigushi, Recognizable closures and submonoids of free partially commutative monoids, Theoret. Comput. Sci. 86, p233–241, 1991.

    Google Scholar 

  14. M. Linna, Finite Power Property of regular languages, Automata, Languages and Programming, 1973.

    Google Scholar 

  15. A. Mazurkiewicz, Concurrent program schemes and their interpretations, Aarhus university, DAIMI rep. PB 78, 1977.

    Google Scholar 

  16. A. Mazurkiewicz, Traces, Histories, Graphs: instances of a process monoid, Lecture Notes in Computer Science 176, p254–264, 1984.

    Google Scholar 

  17. Y. Métivier, Une condition suffisante de reconnaissabilité dans un monoÏde partiellement commutatif, RAIRO Theoretical Informatics and Applications 20, p121–127, 1986.

    Google Scholar 

  18. Y. Métivier, On recognizable subset of free partially Commutative Monoids, Theoret. Comput. Sci. 58, p201–208, 1988.

    Google Scholar 

  19. Y. Métivier and B. Rozoy, On the star operation in free partially commutative monoids, International Journal of Foundations of Computer Science 2, p257–265, 1991.

    Google Scholar 

  20. Y. Métivier and G. Richomme, On the star operation and the finite power property in free partially commutative monoid, Internal Report LaBRI-Université Bordeaux I 93–15, 1993.

    Google Scholar 

  21. E. Ochmański, Notes on a star mystery, Bulletin of EATCS 40, p252–257, February 1990.

    Google Scholar 

  22. J. Sakarovitch, The “last” decision problem for rational trace languages, Proceedings of LATIN'92, Lecture Notes in Computer Science 583, p460–473, 1992.

    Google Scholar 

  23. A. Salomaa, Jewels of formal languages theory, PITMAN eds.

    Google Scholar 

  24. I. Simon, Limited subsets of a free monoid, Proceedings of th 19th FOCS, p143–150, 1978.

    Google Scholar 

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Authors and Affiliations

  1. LaBRI, Université Bordeaux I, ENSERB, 351 cours de la Libération, 33405, Talence, France

    Yves Métivier & GwénaËl Richomme

Authors
  1. Yves Métivier
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  2. GwénaËl Richomme
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Patrice Enjalbert Ernst W. Mayr Klaus W. Wagner

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© 1994 Springer-Verlag Berlin Heidelberg

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Métivier, Y., Richomme, G. (1994). On the star operation and the finite power property in free partially commutative monoids. In: Enjalbert, P., Mayr, E.W., Wagner, K.W. (eds) STACS 94. STACS 1994. Lecture Notes in Computer Science, vol 775. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57785-8_153

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  • DOI: https://doi.org/10.1007/3-540-57785-8_153

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57785-0

  • Online ISBN: 978-3-540-48332-8

  • eBook Packages: Springer Book Archive

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