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The time and tape complexity of developmental languages

  • I. H. Sudborough
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 52)

Abstract

The following results are established:
  1. (1)

    EDOL \( \subseteq \) DSPACE (log n)

     
  2. (2)

    EOL \( \subseteq \) DSPACE ((log n)2)

     
  3. (3)

    EDTOL \( \subseteq \) NSPACE (log n)

     
  4. (4)

    EDTOL \( \subseteq \) DSPACE (log n) if and only if NSPACE (log n) \( \subseteq \) DSPACE (log n)

     

Statement (4) follows from statement (3) above, the fact that all linear context-free languages are EDTOL languages [21], and the existence of a linear context-free language which is log-tape complete for NSPACE (log n) [15]. Furthermore, it is shown that all EOL languages are log-tape reducible to context-free languages. Hence, EOL \( \subseteq \) DSPACE (log n) if and only if every context-free language is in DSPACE (log n).

Keywords

Turing Machine Input String Derivation Tree Membership Problem Input Tape 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. (1).
    I.H. Sudborough, On the Tape Complexity of Deterministic Context-Free Languages, to appear. Some of these results are in "On Deterministic Context-Free Languages, Multihead Automata, and the Power of an Ausiliary Pushdown Store," Proceedings of the 8th Annual ACM Symposium on Theory of Computing (1976), 141–148.Google Scholar
  2. (2).
    I.H. Sudborough, The Complexity of the Membership Problem for Some Extensions of Context-Free Languages, Intern. J. Computer Math., to appear.Google Scholar
  3. (3).
    P.M. Lewis, R.E. Stearns, and J. Hartmanis, Memory Bounds for the Recognition of Context-Free and Context-Sensitive Languages, Proceedings of the Sixth Annual IEEE Symposium on Switching Circuit Theory and Logical Design (1965), 199–212.Google Scholar
  4. (4).
    S.A. Greibach, The Hardest Context-Free Language, SIAM J. on Computing 2 (1973), 304–310.Google Scholar
  5. (5).
    I.H. Sudborough, On Tape-Bounded Complexity Classes and Multi-Head Finite Automata, JCSS (1975), 62–76.Google Scholar
  6. (6).
    G.T. Herman and G. Rozenberg, Developmental Systems and Languages, North Holland Publishers, Amsterdam, 1975.Google Scholar
  7. (7).
    J. Van Leeuwen, The Tape Complexity of Context-Independent Developmental Languages, JCSS (1975), 203–211.Google Scholar
  8. (8).
    J. Van Leeuwen, The Membership Questions for ETOL-languages is Polynomial Complete, Info. Processing Letters 3 (1975), 138–143.Google Scholar
  9. (9).
    J.E. Hopcraft and J.D. Ullman, Formal Languages and Their Relation to Automata, Addison-Wesley Publishing Co., Reading, Mass., 1969.Google Scholar
  10. (10).
    N.D. Jones, Space-Bounded Reducibility among Combinational Problems, JCSS 11 (1975), 62–85.Google Scholar
  11. (11).
    A.R. Meyer and L.J. Stockmeyer, Word Problems Requiring Exponential Time, Proceedings of Fifth Annual ACM Symposium on Theory of Computing (1973), 1–9.Google Scholar
  12. (12).
    S.A. Cook, Characteristics of Pushdown Machines in Terms of Time-Bounded Computers, JACM 18 (1971), 4–18.Google Scholar
  13. (13).
    W.J. Savitch, Relationships Between Nondeterministic and Deterministic Tape Complexities, JCSS 4,2 (1970), 177–192.Google Scholar
  14. (14).
    A.V. Aho and J.D. Ullman, The Theory of Parsing, Translation, and Compiling, Vol. I, Prentice-Hall Publishing Co., Englewood Cliffs, N.J., 1972.Google Scholar
  15. (15).
    I.H. Südborough, On Tape-Bounded Complexity Classes and Linear Context-Free Languages, JACM (1975), 500–501.Google Scholar
  16. (16).
    S.A. Cook, Path Systems and Language Recognition, Proceedings of Second Annual ACM Symposium on Theory of Computing (1970), pp. 70–72.Google Scholar
  17. (17).
    A.K. Arora and I.H. Sudborough, On Languages log-tape reducible to context-free languages, Proceedings of the 1976 Conference on Information Sciences and Systems, Johns Hopkins University, Baltimore, Maryland, 1976.Google Scholar
  18. (18).
    T. Harju, personal communication.Google Scholar
  19. (19).
    T. Harju, A polynomial recognition algorithm for the EDTOL languages, Elektron. Informationsverarbeit. Kybernetik, to appear.Google Scholar
  20. (20).
    E.N.D. Jones and E.S. Skyum, Recognition of deterministic ETOL languages in polynomial time, Technical Report DAIMI PB-63 (October, 1976), Institute of Mathematics, University of Aarhus, 8000 Aarhus C, Denmark.Google Scholar
  21. (21).
    A. Salomaa, Parallelism in rewriting systems, in Automata, Languages and Programming, J. Loeckx (ed.), Springer-Verlag Lecture Notes in Computer Science Series 14 (1974), pp. 523–533.Google Scholar
  22. (22).
    J. Van Leeuwen, Notes on pre-set pushdown automata, in L Systems, G. Rozenberg and A. Salomaa (eds.), Springer-Verlag Lecture Notes in Computer Science Series 15 (1974), pp. 177–188.Google Scholar
  23. (23).
    G. Rozenberg and P. Doucet, on OL-Languages, Information and Control 19, 1971, pp. 302–318.Google Scholar
  24. (24).
    P.M.B. Vitányi, On the size of DOL languages, in L systems, G. Rozenberg and A. Salomaa (eds.), Springer-Verlag Lecture Notes in Computer Science Series 15 (1974), pp. 78–92.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1977

Authors and Affiliations

  • I. H. Sudborough
    • 1
  1. 1.Department of Computer Sciences The Technological InstituteNorthwestern UniversityEvanston

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