Nothing Special   »   [go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

Deterministic asynchronous automata for infinite traces

  • Published:
Acta Informatica Aims and scope Submit manuscript

Abstract

This paper shows the equivalence between the family of recognizable languages over infinite traces and the family of languages which are recognized by deterministic asynchronous cellular Muller automata. We thus give a proper generalization of McNaughton's Theorem from infinite words to infinite traces. Thereby we solve one of the main open problems in this field. As a special case we obtain that every closed (w.r.t. the independence relation) word language is accepted by someI-diamond deterministic Muller automaton.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • [Arn85] Arnold, A.: A syntactic congruence for rational ω-languages. Theoret. Comput. Sci.39, 333–335 (1985)

    Google Scholar 

  • [CF69] Cartier, P., Foata, D.: Problèmes combinatoires de commutation et réarrangements. (Lect. Notes Math., vol. 85) Berlin, Heidelberg, New York: Springer 1969

    Google Scholar 

  • [CMZ89] Cori, R., Métivier, Y., Zielonka, W.: Asynchronous mappings and asynchronous cellular automata. Tech. rep. 89-97, LABRI, Univ. Bordeaux, 1989

  • [CP85] Cori, R., Perrin, D.: Automates et commutations partielles. R.A.I.R.O.—Inf. Théor. Appl.19, 21–32 (1985)

    Google Scholar 

  • [Die90] Diekert, V.: Combinatorics on traces. (Lect. Notes Comput. Sci., vol. 454) Berlin, Heidelberg, New York: Springer 1990

    Google Scholar 

  • [Die91] Diekert, V.: On the concatenation of infinite traces. In: Choffrut C. et al. (eds.) Proceedings of the 8th Annual Symposium on Theoretical Aspects of Computer Science (STACS'91), Hamburg 1991 (Lect. Notes Comput. Sci., vol. 480, pp. 105–117) Berlin, Heidelberg, New York: Springer 1991. Also in Theoret. Comput. Sci.113, 35–54 (1993)

    Google Scholar 

  • [Gas91] Gastin, P.: Recognizable and rational trace languages of finite and infinite traces. In: Choffrut C. et al. (eds.) Proceedings of the 8th Annual Symposium on Theoretical Aspects of Computer Science (STACS'91), Hamburg 1991 (Lect. Notes Comput. Sci., vol. 480, pp. 89–104) Berlin, Heidelberg, New York: Springer 1991

    Google Scholar 

  • [GP92] Gastin, P., Petit, A.: Asynchronous cellular automata for infinite traces. In: W. Kuich (ed.) Proceedings of the 19th International Colloquium on Automata Languages and Programming (ICALP'92), Vienna (Austria) 1992 (Lect. Notes Comput. Sci., vol. 623) Berlin, Heidelberg, New York: Springer 1992 Also available as Tech. Rep. 91-68, LITP, Université Paris 6, France, 1991

    Google Scholar 

  • [GPZ91] Gastin, P., Petit, A., Zielonka, W.: A Kleene theorem for infinite trace languages, In: Albert J.L. et al. (eds.) Proceedings of the 18th International Colloquium on Automata Languages and Programming (ICALP'91), Madrid (Spain) 1991 (Lect. Notes Comput. Sci., vol. 510, pp. 254–266) Berlin, Heidelberg, New York: Springer 1991

    Google Scholar 

  • [GR91] Gastin, P., Rozoy, B.: The poset of infinitary traces. Tech. Rep. LITP 91.07, Université Paris 6 (France), 1991. Also in Theoret. Comput. Sci.120, 101–121 (1993)

  • [Kwi90] Kwiatkowska, M.: A metric for traces. Inf. Process. Lett.35, 129–135 (1990)

    Google Scholar 

  • [Maz77] Mazurkiewicz, A.: Concurrent program schemes and their interpretations. DAIMI Rep. PB 78, Aarhus University, Aarhus, 1977

    Google Scholar 

  • [Maz87] Mazurkiewicz, A.: Trace theory. In: Brauer, W. et al. (eds.) Petri Nets, Applications and Relationship to other Models of Concurrency (Lect. Notes Comput. Sci., vol. 255, pp. 279–324) Berlin, Heidelberg, New York: Springer 1987

    Google Scholar 

  • [McN66] McNaughton, R.: Testing and generating infinite sequences by a finite automaton. Inf. Control9, 521–530 (1966)

    Google Scholar 

  • [PP91] Perrin, D., Pin, J.E.: Mots Infinis. Tech. Rep. LITP 91.06, Université Paris 6 (France), 1992 (Book to appear)

  • [Tho90] Thomas, W.: Automata on infinite objects. In: van Leeuwen, J. (ed.) Handbook of theoretical computer science, pp. 133–191. Amsterdam: Elsevier 1990

    Google Scholar 

  • [Zie87] Zielonka, W.: Notes on finite asynchronous automata. R.A.I.R.O.—Inf. Théor. Appl.21, 99–135 (1987)

    Google Scholar 

  • [Zie89] Zielonka, W.: Safe executions of recognizable trace languages by asynchronous automata. In: Mayer A.R. et al. (eds.) Proceedings Symposium on Logical Foundations of Computer Science, Logic at Botik '89, Pereslavl-Zalessky (USSR) 1989 (Lect. Notes Comput. Sci., vol. 363, pp. 278–289) Berlin, Heidelberg, New York: Springer 1989

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Informatik, Universität Stuttgart, Breitwiesenstrasse 20-22, D-70565, Stuttgart, Germany

    Volker Diekert & Anca Muscholl

Authors
  1. Volker Diekert
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Anca Muscholl
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research has been supported by the ESPRIT Basic Research Action No. 6317 ASMICS 2.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Diekert, V., Muscholl, A. Deterministic asynchronous automata for infinite traces. Acta Informatica 31, 379–397 (1994). https://doi.org/10.1007/BF01178512

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01178512

Keywords

Search

Navigation