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Context-Free Languages of Countable Words

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Theoretical Aspects of Computing - ICTAC 2009 (ICTAC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5684))

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Abstract

We define context-free grammars with Büchi acceptance condition generating languages of countable words. We establish several closure properties and decidability results for the class of Büchi context-free languages generated by these grammars. We also define context-free grammars with Müller acceptance condition and show that there is a language generated by a grammar with Müller acceptance condition which is not a Büchi context-free language.

Research supported by grant no. K 75249 from the National Foundation of Hungary for Scientific Research.

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References

  1. Bedon, N.: Finite automata and ordinals. Theor. Comp. Sci. 156, 119–144 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bedon, N., Bès, A., Carton, O., Rispal, C.: Logic and rational languages of words indexed by linear orderings. In: Hirsch, E.A., Razborov, A.A., Semenov, A., Slissenko, A. (eds.) CSR 2008. LNCS, vol. 5010, pp. 76–85. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  3. Bès, A., Carton, O.: A Kleene theorem for languages of words indexed by linear orderings. In: De Felice, C., Restivo, A. (eds.) DLT 2005. LNCS, vol. 3572, pp. 158–167. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  4. Bloom, S.L., Choffrut, Ch.: Long words: the theory of concatenation and ω-power. Theor. Comp. Sci. 259, 533–548 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bloom, S.L., Ésik, Z.: Axiomating omega and omega-op powers of words. Theor. Inform. Appl. 38, 3–17 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  6. Bloom, S.L., Ésik, Z.: The equational theory of regular words. Inform. and Comput. 197, 55–89 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  7. Bloom, S.L., Ésik, Z.: Regular and algebraic words and ordinals. In: Mossakowski, T., Montanari, U., Haveraaen, M. (eds.) CALCO 2007. LNCS, vol. 4624, pp. 1–15. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  8. Bruyère, V., Carton, O.: Automata on linear orderings. J. Comput. System Sci. 73, 1–24 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  9. Büchi, J.R.: Weak second-order arithmetic and finite automata. Z. Math. Logik und Grundlagen Math. 6, 66–92 (1960)

    Article  MathSciNet  MATH  Google Scholar 

  10. Büchi, J.R.: The monadic second order theory of ω 1. In: Decidable theories, II. Lecture Notes in Math., vol. 328, pp. 1–127. Springer, Heidelberg (1973)

    Chapter  Google Scholar 

  11. Choueka, Y.: Finite automata, definable sets, and regular expressions over ω n-tapes. J. Comput. System Sci. 17(1), 81–97 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  12. Cohen, R.S., Gold, A.Y.: Theory of ω-languages, parts one and two. Journal of Computer and System Science 15, 169–208 (1977)

    Article  Google Scholar 

  13. Courcelle, B.: Frontiers of infinite trees. RAIRO Theor. Inf. 12, 319–337 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  14. Doner, J.: Tree acceptors and some of their applications. J. Comput. System Sci. 4, 406–451 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  15. Ésik, Z., Ito, M., Kuich, W.: Linear languages of finite and infinite words (to appear)

    Google Scholar 

  16. Gécseg, F., Steinby, M.: Tree automata. Akadémiai Kiadó, Budapest (1984)

    Google Scholar 

  17. Heilbrunner, S.: An algorithm for the solution of fixed-point equations for infinite words. RAIRO Theor. Inf. 14, 131–141 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  18. Nivat, M.: Sur les ensembles de mots infinis engendrés par une grammaire algébrique (French). RAIRO Inform. Théor. 12(3), 259–278 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  19. Perrin, D., Pin, J.-E.: Infinite Words. Elsevier, Amsterdam (2004)

    MATH  Google Scholar 

  20. Rabin, M.O.: Decidability of second-order theories and automata on infinite trees. Trans. Amer. Math. Soc. 141, 1–35 (1969)

    MathSciNet  MATH  Google Scholar 

  21. Rosenstein, J.G.: Linear Orderings. Academic Press, London (1982)

    MATH  Google Scholar 

  22. Thatcher, J.W., Wright, J.B.: Generalized finite automata theory with an application to a decision problem of second-order logic. Math. Systems Theory 2, 57–81 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  23. Thomas, W.: On frontiers of regular sets. RAIRO Theor. Inf. 20, 371–381 (1986)

    Article  MATH  Google Scholar 

  24. Thomas, W.: Automata on infinite objects. In: Handbook of Theoretical Computer Science, vol. B, pp. 135–191. Elsevier, Amsterdam (1990)

    Google Scholar 

  25. Wojciechowski, J.: Classes of transfinite sequences accepted by finite automata. Fundamenta Informaticæ 7, 191–223 (1984)

    MathSciNet  MATH  Google Scholar 

  26. Wojciechowski, J.: Finite automata on transfinite sequences and regular expressions. Fundamenta Informaticæ 8, 379–396 (1985)

    MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Dept. of Computer Science, University of Szeged, Hungary

    Zoltán Ésik & Szabolcs Iván

Authors
  1. Zoltán Ésik
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  2. Szabolcs Iván
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Editor information

Editors and Affiliations

  1. Institut für Informatik, TU München, Boltzmannstr. 3, 85748, Garching, Germany

    Martin Leucker

  2. School of Computer Science and Engineering, University of New South Wales, Sydney, Australia

    Carroll Morgan

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Ésik, Z., Iván, S. (2009). Context-Free Languages of Countable Words . In: Leucker, M., Morgan, C. (eds) Theoretical Aspects of Computing - ICTAC 2009. ICTAC 2009. Lecture Notes in Computer Science, vol 5684. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03466-4_12

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  • DOI: https://doi.org/10.1007/978-3-642-03466-4_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03465-7

  • Online ISBN: 978-3-642-03466-4

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