Abstract
The following results are established:
-
(1)
EDOL \( \subseteq \) DSPACE (log n)
-
(2)
EOL \( \subseteq \) DSPACE ((log n)2)
-
(3)
EDTOL \( \subseteq \) NSPACE (log n)
-
(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).
This work is supported by NSF Grant GJ-43228
Chapter PDF
Similar content being viewed by others
Keywords
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
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.
I.H. Sudborough, The Complexity of the Membership Problem for Some Extensions of Context-Free Languages, Intern. J. Computer Math., to appear.
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.
S.A. Greibach, The Hardest Context-Free Language, SIAM J. on Computing 2 (1973), 304–310.
I.H. Sudborough, On Tape-Bounded Complexity Classes and Multi-Head Finite Automata, JCSS (1975), 62–76.
G.T. Herman and G. Rozenberg, Developmental Systems and Languages, North Holland Publishers, Amsterdam, 1975.
J. Van Leeuwen, The Tape Complexity of Context-Independent Developmental Languages, JCSS (1975), 203–211.
J. Van Leeuwen, The Membership Questions for ETOL-languages is Polynomial Complete, Info. Processing Letters 3 (1975), 138–143.
J.E. Hopcraft and J.D. Ullman, Formal Languages and Their Relation to Automata, Addison-Wesley Publishing Co., Reading, Mass., 1969.
N.D. Jones, Space-Bounded Reducibility among Combinational Problems, JCSS 11 (1975), 62–85.
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.
S.A. Cook, Characteristics of Pushdown Machines in Terms of Time-Bounded Computers, JACM 18 (1971), 4–18.
W.J. Savitch, Relationships Between Nondeterministic and Deterministic Tape Complexities, JCSS 4,2 (1970), 177–192.
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.
I.H. Südborough, On Tape-Bounded Complexity Classes and Linear Context-Free Languages, JACM (1975), 500–501.
S.A. Cook, Path Systems and Language Recognition, Proceedings of Second Annual ACM Symposium on Theory of Computing (1970), pp. 70–72.
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.
T. Harju, personal communication.
T. Harju, A polynomial recognition algorithm for the EDTOL languages, Elektron. Informationsverarbeit. Kybernetik, to appear.
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.
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.
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.
G. Rozenberg and P. Doucet, on OL-Languages, Information and Control 19, 1971, pp. 302–318.
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.
Author information
Authors and Affiliations
Editor information
Copyright information
© 1977 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sudborough, I.H. (1977). The time and tape complexity of developmental languages. In: Salomaa, A., Steinby, M. (eds) Automata, Languages and Programming. ICALP 1977. Lecture Notes in Computer Science, vol 52. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-08342-1_40
Download citation
DOI: https://doi.org/10.1007/3-540-08342-1_40
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-08342-9
Online ISBN: 978-3-540-37305-6
eBook Packages: Springer Book Archive