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Restarting Tree Automata and Linear Context-Free Tree Languages

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Algebraic Informatics (CAI 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4728))

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Abstract

We derive a normal form for linear context-free tree grammars that involves only growing productions. Based on this normal form we then show that all linear context-free tree languages are recognized by restarting tree automata which utilize auxiliary symbols.

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References

  1. Arnold, A., Dauchet, M.: Un théorème de duplication pour les forêts algébriques. Journal of Computer and System Sciences 13, 223–244 (1976)

    MATH  MathSciNet  Google Scholar 

  2. Aho, A.V.: Indexed grammars—An extension of context-free grammars. Journal of the ACM 15, 647–671 (1968)

    Article  MATH  MathSciNet  Google Scholar 

  3. Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, Cambridge (1998)

    Google Scholar 

  4. Fischer, M.J.: Grammars with macro-like productions. In: IEEE Conf. Record, 9th Ann. Symp. on Switching and Automata Theory, pp. 131–142. IEEE Computer Society Press, Los Alamitos (1968)

    Google Scholar 

  5. Fujiyoshi, A.: Restrictions on monadic context-free tree grammars. In: COLING 2004, Proc., pp. 78–84 (2004)

    Google Scholar 

  6. Fujiyoshi, A.: Linearity and nondeletion on monadic context-free tree grammars. Information Processing Letters 93, 103–107 (2005)

    Article  MathSciNet  Google Scholar 

  7. Fujiyoshi, A., Kasai, T.: Spinal-formed context-free tree grammars. Theory of Computing Systems 33, 59–83 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  8. Guessarian, I.: Pushdown tree automata. Mathematical Systems Theory 16, 237–263 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  9. Jančar, P., Mráz, F., Plátek, M., Vogel, J.: On restarting automata with rewriting. In: Păun, G., Salomaa, A. (eds.) New Trends in Formal Languages. LNCS, vol. 1218, pp. 119–136. Springer, Heidelberg (1997)

    Google Scholar 

  10. Kepser, S., Mönnich, U.: Closure properties of linear context-free tree languages with an application to optimality theory. Theoretical Computer Science 354, 82–97 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  11. Maibaum, T.S.E.: A generalized approach to formal languages. Journal of Computer and System Sciences 8, 409–439 (1974)

    MATH  MathSciNet  Google Scholar 

  12. Maibaum, T.S.E.: Pumping lemmas for term languages. Journal of Computer and System Sciences 17, 319–330 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  13. Otto, F.: Restarting automata and their relations to the Chomsky hierarchy. In: Ésik, Z., Fülöp, Z. (eds.) DLT 2003. LNCS, vol. 2710, pp. 55–74. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  14. Rounds, W.C.: Tree-oriented proofs of some theorems on context-free and indexed languages. In: Second Annual ACM Symp. on Theory of Computing, Proc., pp. 109–116. ACM Press, New York (1970)

    Chapter  Google Scholar 

  15. Schimpf, K.M., Gallier, J.H.: Tree pushdown automata. Journal of Computer and System Sciences 30, 25–40 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  16. Seki, H., Kato, Y.: On the generative power of multiple context-free grammars and macro grammars. Information Science Technical Report, NAIST-IS-TR2006007, Nara Institute of Science and Technology (2006)

    Google Scholar 

  17. Stamer, H., Otto, F.: Restarting tree automata. In: van Leeuwen, J., Italiano, G.F., van der Hoek, W., Meinel, C., Sack, H., Plášil, F. (eds.) SOFSEM 2007. LNCS, vol. 4362, pp. 510–521. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  18. Vijay-Shankar, K., Weir, D.J.: The equivalence of four extensions of context-free grammars. Mathematical Systems Theory 27, 511–546 (1994)

    Article  MathSciNet  Google Scholar 

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Symeon Bozapalidis George Rahonis

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Stamer, H., Otto, F. (2007). Restarting Tree Automata and Linear Context-Free Tree Languages. In: Bozapalidis, S., Rahonis, G. (eds) Algebraic Informatics. CAI 2007. Lecture Notes in Computer Science, vol 4728. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75414-5_18

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  • DOI: https://doi.org/10.1007/978-3-540-75414-5_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-75413-8

  • Online ISBN: 978-3-540-75414-5

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