Skip to main content
SpringerLink
Log in

The extended equivalence problem for a class of non-real-time deterministic pushdown automata

  • Published:
Acta Informatica Aims and scope Submit manuscript

Abstract

We propose a new class of non-real-time deterministic pushdown automata (dpda's), named dpda's having the weak segmental property (WSP), and show that the equivalence problem is solvable for two dpda's, one of which is in this class. The equivalence checking algorithm to prove this problem is a further extended direct branching algorithm of Tomita; and with the new skipping step combined with the type B′ replacement of Oyamaguchi, Inagaki and Honda. The algorithm is still relatively simple. The class of dpda's given above is one of the widest known subclasses of proper dpda's (introduced by Ukkonen); with the decidable extended equivalence problem.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Courcelle, B.: An axiomatic approach to the Korenjak-Hopcroft algorithm. Math. Systems Theory16, 191–231 (1983)

    Google Scholar 

  2. Culik II, K., Karhumäki, J.: Synchronizable deterministic pushddown automata and the decidability of their equivalence. Acta Informatica23, 597–605 (1986)

    Google Scholar 

  3. Harrison, M.A.: Introduction to Formal Language Theory. Addison-Wesley (1978)

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

    Google Scholar 

  5. Itzhaik, Y., Yehudai, A.: New families of non real time dpda's and their decidable results. Theoret. Comput. Sci.34, 255–274 (1984)

    Google Scholar 

  6. Korenjak, A.J., Hopcroft, J.E.: Simple deterministic languages. Proc. IEEE 7th SWAT, 36–46, Berkeley, CA. (1966)

  7. Oyamaguchi, M., Inagaki, Y., Honda, N.: The equivalence problem for two dpda's, one of which is a finite-turn or one-counter machine. J. Comput. System Sci.23, 366–382 (1981)

    Google Scholar 

  8. Oyamaguchi, M.: Some remarks on subclass containment problems for several classes of dpda's. Inf. Process. Lett.19, 9–12 (1984)

    Google Scholar 

  9. Oyamaguchi, M.: The equivalence problem for real-time deterministic pushdowm automata. J. Assoc. Comput. Mach.34, 731–760 (1987)

    Google Scholar 

  10. Sekimoto, S.: A restricted result on the equivalence problem for deterministic pushdown automata. Trans. IECE JapanJ64-D, 661–668 (1981)

    Google Scholar 

  11. Tomita, E.: A direct branching algorithm for checking equivalence of some classes of deterministic pushdown automata. Inform. Control52, 187–238 (1982)

    Google Scholar 

  12. Tomita, E.: A direct branching algorithm for checking equivalence of strict derministic vs. LL(k) grammars. Theoret. Comput. Sci.23, 129–154 (1983)

    Google Scholar 

  13. Tomita, E.: An extended direct branching algorithm for checking equivalence of deterministic pushdown automata. Theoret. Comput. Sci.32, 87–120 (1984)

    Google Scholar 

  14. Tomita, E., Seino, K.: A weaker sufficient condition for the equivalence of a pair of dpda's to be decidable. Theoret. Comput. Sci.41, 223–230 (1985)

    Google Scholar 

  15. Tomita, E., Seino, K.: A direct branching algorithm for checking the equivalence of two deterministic pushdown transducers, one of which is real-time strict. Theoret. Comput. Sci.64, 39–53 (1989)

    Google Scholar 

  16. Tomita, E., Seino, K.: The extended equivalence problem for a class of non-real-time deterministic pushdown automata. Technical Report UEC CAS94-2, Department of Communications and Systems Engineering, The University of Electro-Communications (1994)

  17. Ukkonen, E.: The equivalence problem for some non-real-time deterministic pushdown automata. J. Assoc. Comput. Mach.29, 1166–1181 (1982)

    Google Scholar 

  18. Valiant, L.G.: Decision procedures for families of deterministic pushdown automata. Ph.D. Thesis, Department of Computer Science, University of Warwick (1973)

  19. Yehudai, A.: A hierarchy of real-time deterministic languages and their equivalence. J. Comput. System Sci.24, 91–100 (1982)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Communications and Systems Engineering, The University of Electro-Communications, Chofugaoka, 182, Chofu, Tokyo, Japan

    Etsuji Tomita & Kazushi Seino

Authors
  1. Etsuji Tomita
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kazushi Seino
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was supported in part by Grants-in-Aid for Scientific Research Nos. 58550240 and 62550259 from the Ministry of Education, Science and Culture, Japan.

Presently with the Ome Works, Toshiba Corporation, Ome, Tokyo 198, Japan.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tomita, E., Seino, K. The extended equivalence problem for a class of non-real-time deterministic pushdown automata. Acta Informatica 32, 395–413 (1995). https://doi.org/10.1007/BF01178385

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01178385

Keywords

Search

Navigation