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Asynchronous cellular automata for infinite traces

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Automata, Languages and Programming (ICALP 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 623))

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Abstract

The notion of infinite traces has been proposed to generalize both the finite traces defined by Mazurkicwicz and the infinite words. The family of recognizable languages of infinite traces has been introduced by means of recognizing morphisms and characterized by c-rational expressions. In this paper, we provide another characterization of this family using asynchronous cellular automata (which carry the most intuitive idea of finite suite concurrent machines). To this purpose, we give effective constructions for c-rational operations on these automata, which are of independent interest.

This work has been partly supported by the ESPRIT Basic Research Actions N∘ 3166 (ASMICS) and N∘ 3148 (DEMON) and by the PRC C3 and Math-Info.

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References

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

    Article  Google Scholar 

  2. J. BERSTEL, “Transductions and context free languages”, Teubner Studienbucher Informatik, 1979.

    Google Scholar 

  3. P. BONIZZONI, G. MAURI and G. PIGHIZZINI, “About infinite traces”, Proceedings of the ASMICS Workshop on Partially Commutative Monoids, Tech. Rep. TUM-I9002, Technische Universität München, 1989.

    Google Scholar 

  4. R. CORI, Y. METIVIER and W. ZIELONKA, “Asynchronous mappings and asynchronous cellular automata”, Tech. Rep. 89-97, LaBRI, Université de Bordeaux, France, 1989.

    Google Scholar 

  5. V. DIEKERT, “Combinatorics on traces”, Lecture Notes in Computer Science 454, 1990.

    Google Scholar 

  6. V. DIEKERT, “On the concatenation of infinite traces”, STACS'91, Lecture Notes in Computer Science 480, p. 105–117, 1991.

    Google Scholar 

  7. V. DIEKERT, P. GASTIN, A. PETIT, “Recognizable complex trace languages”, MFCS'91, Lecture Notes in Computer Science 520, p. 131–140, 1991.

    Google Scholar 

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

    Google Scholar 

  9. P. GASTIN, “Infinite traces”, Proceedings of the Spring School of Theoretical Computer Science on “Semantics of concurrency”, Lecture Notes in Computer Science 469, p. 277–308, 1990.

    Google Scholar 

  10. P. GASTIN, “Recognizable and rational languages of finite and infinite traces”, STACS'91, Lecture Notes in Computer Science 480, p. 89–104, 1991.

    Google Scholar 

  11. P. GASTIN and A. PETIT, “Asynchronous automata for infinite traces”, Tech. rep. 91.68, LITP, Université Paris 6, France, 1991.

    Google Scholar 

  12. P. GASTIN, A. PETIT, W. ZIELONKA, “A Kleene theorem for infinite trace languages”, ICALP'91, Lecture Notes in Computer Science 510, p. 254–266, 1991.

    Google Scholar 

  13. P. GASTIN and B. ROZOY, “The Poset of infinitary traces”, to appear in Theoretical Computer Science, Tech. Rep. 91-07, LITP, Université Paris 6, France, 1991.

    Google Scholar 

  14. M.Z. KWIATKOWSKA, “A metric for traces”, Information and Processing Letters 35, p. 129–135, 1990.

    Google Scholar 

  15. A. MPAZURKIEWICZ, “Concurrent program Schemes and their interpretations”, Aarhus University, DAIMI Rep. PB 78, 1977.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  19. D. PERRIN and J.E. PIN, “Mots Infinis”, Tech. Rep. 91-06, LITP, Université Paris 6, France, 1991. Book to appear.

    Google Scholar 

  20. G. PIGHIZZINI, “On the iteration of trace languages”, Proceed. of the ASMICS Workshop on Infinite Traces, to appear as Tech. Rep., Universität Stuttgart, 1992.

    Google Scholar 

  21. 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, p. 172–182, 1989.

    Google Scholar 

  22. W. THOMAS, “Automata on infinite objects”, Handbook of Theoretical Computer Science (J.V. Leeuwen, Ed.), Elsevier, Amsterdam, Vol. B, p. 135–191, 1990.

    Google Scholar 

  23. W. THOMAS, “On logics, tilings, and automata”, ICALP'91, Lecture Notes in Computer Science 510, p. 441–454, 1991.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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Authors and Affiliations

  1. Institut Blaise Pascal, Université PARIS 6 LITP, 4, place Jussieu, 75 252, Paris Cedex 05, France

    Paul Gastin

  2. Université PARIS SUD LRI, URA CNRS 410, Bât. 490, 91 405, Orsay Cedex, France

    Antoine Petit

Authors
  1. Paul Gastin
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  2. Antoine Petit
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W. Kuich

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© 1992 Springer-Verlag Berlin Heidelberg

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Gastin, P., Petit, A. (1992). Asynchronous cellular automata for infinite traces. In: Kuich, W. (eds) Automata, Languages and Programming. ICALP 1992. Lecture Notes in Computer Science, vol 623. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55719-9_106

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  • DOI: https://doi.org/10.1007/3-540-55719-9_106

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  • Print ISBN: 978-3-540-55719-7

  • Online ISBN: 978-3-540-47278-0

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