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Semi-groups acting on context-free graphs

  • Session 4: Languages and Processes
  • Conference paper
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Automata, Languages and Programming (ICALP 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1099))

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Abstract

Let Γ be a context-free graph. We give sufficient conditions on a semi-group of bisimulations H to ensure that the quotient HΓ is context-free. Using these sufficient conditions we show that the quotient Aut(Γ)Γ of Γ by its full group of automorphisms is always context-free.

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References

  1. A. V. Anisimov. Group languages. Kibernetica 4, pages 18–24, 1971.

    Google Scholar 

  2. A. Arnold and A. Dicky. Transition systems equivalence. Information and Computation 82, pages 198–229, 1989.

    Article  Google Scholar 

  3. J. Baeten, J. Bergstra, and J. Klop. Decidability of bisimulation equivalence for processes generating context-free languages. In Proceedings of PARLE 87, LNCS 259, pages 94–111. 1987.

    Google Scholar 

  4. H. Bass and J.P. Serre. Arbres, amalgames, SL2. SMF, collection astérisque, nr 46, 1983.

    Google Scholar 

  5. M. Bauderon. Infinite hypergraph I, basic properties (fundamental study). TCS 82, pages 177–214, 1991.

    Google Scholar 

  6. M. Bauderon. Infinite hypergraph II, systems of recursive equations. TCS 103, pages 165–190, 1992.

    Google Scholar 

  7. J. Berstel and L. Boasson. Context-free languages. In Handbook of theoretical computer science, vol. B, Chapter 2, pages 59–102. Elsevier, 1991.

    Google Scholar 

  8. D. Caucal. Graphes canoniques de graphes algébriques. RAIRO TIA, nr 24-4, pages 339–352, 1990.

    Google Scholar 

  9. D. Caucal. On the regular structure of prefix rewritings. TCS 106, pages 61–86, 1992.

    Google Scholar 

  10. D. Caucal. Bisimulation of context-free grammars and of pushdown automata. To appear in CSLI, Modal Logic and process algebra, vol. 53, Stanford, pages 1–20, 1995.

    Google Scholar 

  11. S. Christensen, H. Hiittel, and C. Stirling. Bisimulation equivalence is decidable for all context-free processes. In Proceedings of CONCUR 92, LNCS 630, pages 138–147. 1992.

    Google Scholar 

  12. B. Courcelle. The monadic second-order logic of graphs ii: infinite graphs of bounded width. Math. Systems Theory 21, pages 187–221, 1989.

    Google Scholar 

  13. B. Courcelle. Graph rewriting: and algebraic and logic approach. In Jan van Leeuwen, editor, Handbook of Theoretical Computer Science, volume B, pages 193–242, 1990.

    Google Scholar 

  14. B. Courcelle. The monadic second-order logic of graphs IV: definability properties of equational graphs. Annals of Pure and Applied Logic, pages 183–255, 1990.

    Google Scholar 

  15. W. Dicks and M.J. Dunwoody. Groups acting on graphs. Cambridge University Press, 1990.

    Google Scholar 

  16. S. Eilenberg. Automata, Languages and Machines, vol. A. Academic Press, 1974.

    Google Scholar 

  17. C. Frougny and J. Sakarovitch. Synchronized rational relations of finite and infinite words. TCS 108, pages 45–82, 1993.

    Google Scholar 

  18. R. Halin. Automorphisms and endomorphisms of infinite locally finite graphs. Abh. Math. Sem. Univ. Hamburg 39, pages 251–283, 1973.

    Google Scholar 

  19. M.A. Harrison. Introduction To Formal Language Theory. Addison-Wesley, 1978.

    Google Scholar 

  20. Y. Hirshfeld, M. Jerrum, and F. Moller. A polynomial algorithm for deciding bisimilarity of normed context-free processes. In Proceedings of Dagstuhl seminar on Algorithms in Automata theory. To appear in TCS, 1994.

    Google Scholar 

  21. C.M. Hoffmann. Group-theoretic algorithms and graph-isomorphism. LNCS 136, 1982.

    Google Scholar 

  22. D. E. Muller and P. E. Schupp. Groups, the theory of ends and context-free languages. JCSS vol 26, no 3, pages 295–310, 1983.

    Google Scholar 

  23. D. E. Muller and P. E. Schupp. The theory of ends, pushdown automata and second-order logic. TCS 37, pages 51–75, 1985.

    Google Scholar 

  24. D. Park. Concurrency and automata on infinite sequences. LNCS 104, pages 167–183, 1981.

    Google Scholar 

  25. L. Pelecq. Automorphism groups of context-free graphs. Accepted for publication in TCS, pages 1–17, 1995.

    Google Scholar 

  26. G. Senizergues. Graphes context-free. Notes de cours de DEA de l'université de Bordeaux 1, pages 1–98, 1989.

    Google Scholar 

  27. G. Senizergues. Semi-groups acting on context-free graphs. LaBRI internal report nr 1094–95, can be accessed at the URL, http://www.labri.u-bordeaux.fr/, 1995.

    Google Scholar 

  28. G. Sénizergues. The isomorphism problem for the transition-graphs of pushdown automata. Talk given at FAIT 89, Wuerzburg, Germany, December 1989.

    Google Scholar 

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Friedhelm Meyer Burkhard Monien

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© 1996 Springer-Verlag Berlin Heidelberg

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Sénizergues, G. (1996). Semi-groups acting on context-free graphs. In: Meyer, F., Monien, B. (eds) Automata, Languages and Programming. ICALP 1996. Lecture Notes in Computer Science, vol 1099. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61440-0_129

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  • DOI: https://doi.org/10.1007/3-540-61440-0_129

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61440-1

  • Online ISBN: 978-3-540-68580-7

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