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Synchronizable deterministic pushdown automata and the decidability of their equivalence

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Summary

The notion of synchronized and synchronizable deterministic pushdown automata (DPDA's) is introduced. It is shown that the equivalence of two synchronized and even of synchronizable DPDA's can be tested. It is conjectured that every two equivalent DPDA's are synchronizable. It is also shown that the equivalence of two deterministic pushdown transducers whose underlying DPDA's are synchronized can be tested.

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References

  1. Albert, J., Culik II, K., Karhumäki, J.: Test sets for context-free languages and algebraic systems of equations. Inf. Control 52, 172–186 (1982)

    Google Scholar 

  2. Beeri, C.: An improvement on Valiant's decision procedure for equivalence of deterministic finite turn pushdown machines, Theor. Comput. Sci. 3, 305–320 (1976)

    Google Scholar 

  3. Courcelle, B.: An axiomatic approach to the Korenjak-Hopcroft algorithms, in Proc. 8th ICALP, Lect. Notes Comput. Scie. 115, pp. 393–407. Berlin, Heidelberg, New York: Springer 1981

    Google Scholar 

  4. Culik II, K., Karhumäki, J.: Systems of equations over a free monoid and Ehrenfeucht's conjecture, Discrete Math. 43, 139–153 (1983)

    Google Scholar 

  5. Culik II, K., Salomaa, A.: On the decidability of morphic equivalence for languages. J. Comput. Syst. Sci. 17, 163–175 (1978)

    Google Scholar 

  6. Friedman, E.P., Greibach, S.A.: Superdeterministic DPDA's: the method of accepting does affect decision problems. J. Comput. Syst. Sci. 19, 79–117 (1979)

    Google Scholar 

  7. Harrison, M.A., Introduction to formal language theor. Reading, Mass.: Addison-Wesley 1978

    Google Scholar 

  8. Harrison, M.A., Havel, I.M.: Real-time strict deterministic languages, SIAM J. Comput. 1, 333–349 (1972)

    Google Scholar 

  9. Harrison, M.A., Havel, I.M., Yehudai, A.: On equivalence of grammars through transformation trees. Theor. Comput. Sci. 9, 173–205 (1979)

    Google Scholar 

  10. Ibarra, O., Rosier, L.: On the decidability of equivalence for deterministic pushdown transducers. Inf. Process. Lett. 13, 89–93 (1981)

    Google Scholar 

  11. Katayama, T., Tsuchiya, N., Enomoto, H.: On the decidability of equivalence for deterministic pushdown transducers, Trans. Inst. Elect. Commun. Eng. Japan 58-D, 760–767 (1975)

  12. Korenjak, A.J., Hopcroft, J.E., Simple deterministic languages, in Proc. IEEE 7th Annual Symposium on Switching and Automata Theory, 36–46, Berkeley, CA. 1966

  13. Linna, M., Two decidability results for deterministic pushdown automata, J. Comput. Syst. Sic. 18, 92–107(1979)

    Google Scholar 

  14. Olshansky, T., Pnueli, A.: A direct algorithm for checking equivalence of LL(k) grammars, Theor. Comput. Sci. 4, 321–349 (1977)

    Google Scholar 

  15. Oyamaguchi, M., Honda, N.: The decidability of equivalence for deterministic stateless pushdown automata, Inf. Contr. 38, 367–376 (1978)

    Google Scholar 

  16. Oyamaguchi, M., Honda, N., Inagaki, Y.: The equivalence problem for realtime strict deterministic languages, Inf. Control 45, 90–115 (1980)

    Google Scholar 

  17. Rosenkrantz, D.J., Stearns, R.E., Properties of deterministic top-down grammars, Inf. Control 17, 226–256 (1970)

    Google Scholar 

  18. Taniguchi, K., Kasami, T.: A result on the equivalence problem for deterministic pushdown automata, J. Comput. Syst. Sci. 13, 38–50 (1976)

    Google Scholar 

  19. Tomita, E.: A direct branching algorithm for checking equivalence of strict deterministics vs. LL(k) grammars. Theor. Comput. Sci. 23 (1983)

  20. Tomita, E.: A direct branching algorithm for checking equivalence of some classes of deterministic pushdown automata. Inf. Control 52, 187–238 (1982)

    Google Scholar 

  21. Valiant, L.G.: Decision procedures for families of deterministic pushdown automata, Ph.D. Thesis, Department of Computer Science, University of Warwick, Coventry, England 1973

    Google Scholar 

  22. Valiant, L.G.: The equivalence problem for deterministic finite-turn pushdown automata, Inf. Control 25, 123–133 (1974)

    Google Scholar 

  23. Valiant, L.G.: Paterson, M.S., Deterministic one-counter automata. J. Comput. Syst. Sci. 10, 340–350 (1975)

    Google Scholar 

  24. Wood, D.: Some remarks on the KH algorithm for s-grammars. BIT 13, 476–489 (1973)

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Karel Culik II

  2. Department of Mathematics, University of Turku, Turku, Finland

    Juhani Karhumäki

Authors
  1. Karel Culik II
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  2. Juhani Karhumäki
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Additional information

This work was supported by the Natural Sciences and Engineering Research Council of Canada under Grant A-7403.

This work has been done during the second author's visit at the University of Waterloo

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Culik, K., Karhumäki, J. Synchronizable deterministic pushdown automata and the decidability of their equivalence. Acta Informatica 23, 597–605 (1986). https://doi.org/10.1007/BF00288472

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  • DOI: https://doi.org/10.1007/BF00288472

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