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Equivalence of deterministic pushdown automata revisited

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Abstract

This paper briefly analyzes main ideas underlying the comparison algorithm that made it possible to prove the equivalence of deterministic pushdown automata. An example of using this algorithm is presented. The relationship of this algorithm with other results in this area is shown. Moreover, the decidability of problems associated with some classes of formal grammars is established.

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References

  1. S. Ginsburg, The Mathematical Theory of Context-Free Languages [Russian translation], Mir, Moscow (1970).

    MATH  Google Scholar 

  2. D. E. Knuth, “On the translation of languages from left to right,” Inform. and Control, 8, 607–639 (1965).

    Article  MathSciNet  Google Scholar 

  3. M. Harrison and I. Havel, “Strict deterministic grammars,” J. Comp. and System Sci., 7, No. 3, 237–277 (1973).

    MATH  MathSciNet  Google Scholar 

  4. A. J. Korenjac and J. E. Hopcroft, “Simple deterministic languages,” in: Proc. 7th Ann. IEEE Switching and Automata Theory Conf., Berkly (1966), pp. 36–46.

  5. L. G. Valiant, “The equivalence problem for deterministic finite-turn pushdown automata,” Inform. and Control, 25, 123–133 (1974).

    Article  MathSciNet  Google Scholar 

  6. M. Oyamaguchi, “The equivalence problem for real-time D.P.D.A’s,” J. Assoc. Comput. Mach., 34, 731–760 (1987).

    MATH  MathSciNet  Google Scholar 

  7. V. Yu. Romanovskii, “The equivalence problem for real-time deterministic pushdown automata,” Kibernetika, No. 2, 13–23 (1986).

  8. V. Yu. Meitus, “The equivalence problem for real-time strict deterministic pushdown automata,” Kibernetika, No. 5, 14–25 (1989).

  9. D. Rosenkrantz and R. Stearns, “Properties of deterministic topdown grammars,” Inform. and Control., 17, 226–256 (1970).

    Article  MATH  MathSciNet  Google Scholar 

  10. L. Valiant and M. Paterson, “Deterministic one-counter automata,” J. Comput. System Sci., 10, 340–350 (1975).

    MATH  MathSciNet  Google Scholar 

  11. V. Yu. Meitus, “Decidability of the equivalence problem for deterministic pushdown automata,” Cybernetics and Systems Analysis, No. 5, 20–45 (1992).

  12. G. Senizergues, “The equivalence problem for deterministic pushdown automata is decidable,” in: Proc. ICALP 97, Lect. Notes in Comput. Sci., 1256, 671–681 (1997).

  13. G. Senizergues, “L(A) = L(B)? decidability results from complete formal systems,” Theoret. Comput. Sci., 251, 1–166 (2001).

    Article  MATH  MathSciNet  Google Scholar 

  14. A. Aho and J. Ulman, Theory of Parsing, Translation, and Compiling [Russian translation], Vol. 1, Mir, Moscow (1978).

    Google Scholar 

  15. W. Kuich, “Semirings and formal power series: Their relevance to formal languages and automata,” in: G. Rozenberg and A. Salomaa (Eds.), Handbook of Formal Languages, Springer, Berlin (1996), pp. 609–677.

    Google Scholar 

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Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 24–39, March–April 2007.

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Meitus, V.Y. Equivalence of deterministic pushdown automata revisited. Cybern Syst Anal 43, 179–191 (2007). https://doi.org/10.1007/s10559-007-0037-7

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  • DOI: https://doi.org/10.1007/s10559-007-0037-7

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