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Infinitary languages: Basic theory and applications to concurrent systems

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Current Trends in Concurrency

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 224))

Abstract

The aim of this paper is to provide an outlook at this part of the theory of infinitary languages that seems to be essential for understanding the modern theory of concurrent systems. In the first part of this paper we discuss an automata-based approach to infinitary languages. In the second part we turn into applying this theory to concurrent systems as considered within the framework of Petri nets.

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References

  1. Arnold, A.: Topological characterizations of infinite behaviours of transition systems, LNCS Lecture Notes in Computer Science by Springer Verlag 154, 1983.

    Google Scholar 

  2. Arnold, A. and Nivat, M.: Comportement de processus, Report LITP No. 82–12, Univ. Paris 7, 1982.

    Google Scholar 

  3. Boasson, L. and Nivat, N.: Adherences of languages, JCSS 20 (1980) 285–309.

    Google Scholar 

  4. Büchi, J.R.: On a decision method in restricted second-order arithmetic, Proc. Int. Congr. Logic, Math. and Phil.Sci. 1960, Stanford University Press, Stanford, Calif., 1962.

    Google Scholar 

  5. Carstensen, H.: Fairness bei Petrinetzen mit unendlichem Verhalten, Report No. 93, Fachbereich Informatik, Univ. Hamburg, 1982.

    Google Scholar 

  6. Carstensen, H. and Valk, R.: Infinite behaviour and fairness in Petri nets, LNCS Lecture Notes in Computer Science by Springer Verlag 188, 1985.

    Google Scholar 

  7. Choueka, Y.: Theories of ω-automata on ω-tapes: A simplified approach, JCSS 8 (1974) 117–141.

    Google Scholar 

  8. Cohen, R.S. and Gold, A.Y.: Theory of ω-languages, JCSS 15 (1977) 169–208.

    Google Scholar 

  9. Culik II, K. and Salomaa, A.: On infinite words obtained by iterating morphisms, TCS 19 (1982) 29–38.

    Google Scholar 

  10. Eilenberg, S.: Automata, languages and machines, Vol. A, Academic Press, New York, 1974.

    Google Scholar 

  11. Girault-Beauquier, D.: Bilimites de langages reconnaissables, TCS, 33 (1984) 335–342.

    Google Scholar 

  12. Gire, F. and Nivat, N.: Relations rationelles infinitaires, Calcolo 21 (1984) 91–125.

    Google Scholar 

  13. Hack, M.: Petri net languages, Lab.Comp.Sci., MIT, Techn.Rep. 159, Cambridge, Mass., 1972.

    Google Scholar 

  14. Hartmanis, J. and Stearns, R.E.: Sets of numbers defined by finite automata, American Mathematical Monthly 74 (1967) 539–542.

    Google Scholar 

  15. Head, T.: Adherences of DOL languages, TCS 31 (1984) 139–150.

    Google Scholar 

  16. Hedlund, G.A.: Remarks on the work of Axel Thue on sequences, Nordisk Matematisk Tidskrift 16 (1967) 148–150.

    Google Scholar 

  17. Hossley, R.: Finite tree automata and ω-automata, MAC Technical report No. 102, MIT, Cambridge, Mass., 1972.

    Google Scholar 

  18. König, D.: Theorie der endlichen und unendlichen Graphen, Chelsea, New York, 1935.

    Google Scholar 

  19. Landweber, L.H.: Decision problems for ω-automata, Mathematical Systems Theory 3 (1969) 376–384.

    Google Scholar 

  20. Lehman, D., Pnueli, A. and Stavi, J.: Impariality, justice and fairness: the ethics of concurrent termination, LNCS Lecture Notes in Computer Science by Springer Verlag 115, 1981.

    Google Scholar 

  21. Lindner, R. and Staiger, L.: Algebraische Codierungstheorie — Theorie der sequentiellen Codierungen, Akademie, Berlin, 1971.

    Google Scholar 

  22. Linna, M.; On ω-words and ω-computations, Annales Univ. Turkuensis, ser. AI 168, Turku, 1975.

    Google Scholar 

  23. McNaughton, R.: Testing and generating infinite sequences by a finite automaton, Information and Control (1966) 521–530.

    Google Scholar 

  24. Morse, H.M.: Recurrent geodesics on a surface of negative curvature, Transactions of the American Mathematical Society 22 (1921) 84–100.

    Google Scholar 

  25. Muller, D.E.: Infinite sequences and finite machines, AIEE Proc 4th Ann. symp. switch. circ. th. log. design, 1963.

    Google Scholar 

  26. Nivat, M.: Sur les ensembles de mots infinis engendres' par une grammaire algebrique, RAIRO Informatique Theorique 12 (1978) 259–278.

    Google Scholar 

  27. Nivat, M.: Infinitary relations, LNCS Lecture Notes in Computer Science by Springer Verlag 112, 1981.

    Google Scholar 

  28. Nivat, M.: Behaviours of synchronized system of processes, Report LITP No. 81–64, Univ. Paris 7, 1981.

    Google Scholar 

  29. Nivat, M. and Perrin, D.: Ensembles reconnaissables de mots biinfinis, Proc. 14th ACM symp. Th. Computing, 1982.

    Google Scholar 

  30. Automata on infinite words, Edited by M. Nivat and D. Perrin, LNCS Lecture Notes in Computer Science by Springer Verlag 192, 1985.

    Google Scholar 

  31. Park, D.: Concurrency and automata on infinite sequences, LNCS Lecture Notes in Computer Science by Springer Verlag 104, 1981.

    Google Scholar 

  32. Perrin, D.: Recent results on automata and infinite words, LNCS Lecture Notes in Computer Science by Springer Verlag 176, 1984.

    Google Scholar 

  33. Prodinger, H. and Urbanek, F.J.: Language operators related to Init, TCS 8 (1979) 161–175.

    Google Scholar 

  34. Reisig, W.: Petri nets, An introduction, EATCS Monographs on Theoretical Computer Science, Springer-Verlag, Berlin, 1985.

    Google Scholar 

  35. Rozenberg, G. and Thiagarajan, P.S.: Petri nets: Basic notions, structure, behaviour, this volume.

    Google Scholar 

  36. Salomaa, A.: Jewels of formal language theory, Computer Science Press, 1981.

    Google Scholar 

  37. Staiger, L. and Wagner, K.: Automaten theoretische und automatenfreie Characterisierungen topologischer Klassen regulärer Folgenmengen, Elektronische Informationsverarbeitung und Kybernetik 10 (1974) 379–392.

    Google Scholar 

  38. Takahashi, M. and Yamasaki, H.: A note on ω-regular languages, TCS 23 (1983) 217–225.

    Google Scholar 

  39. Thue, A.: Ueber unendliche Zeichenreihen, Videnskabsselskabets Skrifter, I. Mat.-nat. Kl., Kristiania 7 (1906) 1–22.

    Google Scholar 

  40. Valk, R.: Infinite behaviour of Petri nets, TCS 25 (1983) 311–341.

    Google Scholar 

  41. Wagner, K.: On ω-regular sets, Information and Control 43 (1979) 123–177.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Leiden, P.O. Box 9512, 2300 RA, Leiden, The Netherlands

    H. J. Hoogeboom & G. Rozenberg

Authors
  1. H. J. Hoogeboom
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  2. G. Rozenberg
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J. W. de Bakker W. -P. de Roever G. Rozenberg

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© 1986 Springer-Verlag Berlin Heidelberg

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Hoogeboom, H.J., Rozenberg, G. (1986). Infinitary languages: Basic theory and applications to concurrent systems. In: de Bakker, J.W., de Roever, W.P., Rozenberg, G. (eds) Current Trends in Concurrency. Lecture Notes in Computer Science, vol 224. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0027043

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  • DOI: https://doi.org/10.1007/BFb0027043

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16488-3

  • Online ISBN: 978-3-540-39827-1

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