Skip to main content
SpringerLink
Log in

On the complexity of general context-free language parsing and recognition

Extended abstract

  • Conference paper
  • First Online:
Automata, Languages and Programming (ICALP 1979)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 71))

Included in the following conference series:

Abstract

Several results on the computational complexity of general context-free language parsing and recognition are given. In particular we show that parsing strings of length n is harder than recognizing such strings by a factor of only 0(log n), at most. The same is true for linear and/or unambiguous context-free languages. We also show that the time to multiply \(\sqrt n \times \sqrt n\) Boolean Matrices is a lower bound on the time to recognize all prefixes of a string (or do on-line recognition), which in turn is a lower bound on the time to generate a particular convenient representation of all parses of a string (in an ambiguous grammar). Thus these problems are solvable in linear time only if n×n Boolean matrix multiplication can be done in 0(n2).

This research supported by an IBM pre-doctoral fellowship and by NSF grants GJ-474 and MCS77-02474.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  • Adleman, L., K.S. Booth, F.P. Preparata and W.L. Ruzzo, "Improved time and space bounds for Boolean matrix multiplication", Acta Informatica, 11 (1978), 61–70.

    Google Scholar 

  • Aho, A.V., J.E. Hopcroft and J.D. Ullman, The Design and Analysis of Computer Algorithms, Addison-Wesley, Reading, MA (1974).

    Google Scholar 

  • Earley, J., "An efficient context-free parsing algorithm", Comm. ACM 13:1 (1970), 94–102.

    Google Scholar 

  • Fischer, M.J. and A.R. Meyer, "Boolean matrix multiplication and transitive closure", Conference Record IEEE 12th Annual Symposium on Switching and Automata Theory (1971), 129–131.

    Google Scholar 

  • Furman, M.E., "Application of a method of fast multiplication of matrices in the problem of finding the transitive closure of a graph", Soviet Math Dokl. 11:5 (1970), 1252.

    Google Scholar 

  • Gallaire, H., "Recognition time of context free languages by on-line Turing machines", Information and Control 15 (1969), 288–295.

    Google Scholar 

  • Graham, S.L., M.A. Harrison and W.L. Ruzzo, "Online context free language recognition in less than cubic time", Proc. 8th Annual ACM Symposium on Theory of Computing (1976), 112–120.

    Google Scholar 

  • Gray, J. and M.A. Harrison, "On the covering and reduction problems for context-free grammars", JACM 19 (1972), 675–698.

    Google Scholar 

  • Harrison, M.A., Introduction to Formal Language Theory, Addison-Wesley, Reading, MA (1978).

    Google Scholar 

  • Harrison, M.A. and I. Havel, "On the parsing of strict deterministic languages", JACM 21 (1974), 525–548.

    Google Scholar 

  • Hays, D.G., "Automatic language-data processing", in Computer Applications in the Behavioral Sciences, H. Borko (ed.), Prentice-Hall, Englewoods Cliffs, NJ (1962), 394–423.

    Google Scholar 

  • Kasami, T., "An efficient recognition and syntax analysis algorithm for context free languages", Science Report AF CRL-65-758, Air Force Cambridge Research Laboratory, Bedford, MA (1965).

    Google Scholar 

  • Munro, J.I., "Efficient determination of the transitive closure of a directed graph", Information Processing Letters 1:2 (1971), 56–58.

    Google Scholar 

  • Pan, V.Ya., "Strassen's algorithm is not optimal: Trilinear technique of aggregating, uniting and cancelling for constructing fast algorithms for matrix operations", IEEE 19th Annual Symposium on Foundations of Computer Science, (1978), 166–176.

    Google Scholar 

  • Ruzzo, W.L., "General Context-Free Language Recognition". Ph.D. Dissertation, U. C. Berkeley (1978).

    Google Scholar 

  • Strassen, V., "Gaussian elimination is not optimal", Numerische Mathematik 13 (1969), 354–356.

    Google Scholar 

  • Thatcher, J.W., "Characterizing derivation trees of context-free grammars through a generalization of finite automata theory", JCSS 1:4 (1967) 317–322.

    Google Scholar 

  • Thatcher, J.W. and J.B. Wright, "Generalized finite automata theory with an application to a decision problem of second-order logic", Math. Sys. Th. 2:1 (1968) 57–81.

    Google Scholar 

  • Valiant, L., "General context free recognition in less than cubic time", J. Computer and System Sciences 10 (1975), 308–315.

    Google Scholar 

  • Weiner, P., "Linear pattern matching algorithms", Conference Record IEEE 14th Annual Symposium on Switching and Automata Theory (1973), 1–11.

    Google Scholar 

  • Younger, D.H., "Recognition of context-free languages in time n3", Information and Control 10:2 (Feb. 1967), 189–208.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Washington, 98195, Seattle, Washington, USA

    Walter L. Ruzzo

Authors
  1. Walter L. Ruzzo
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Hermann A. Maurer

Rights and permissions

Reprints and permissions

Copyright information

© 1979 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ruzzo, W.L. (1979). On the complexity of general context-free language parsing and recognition. In: Maurer, H.A. (eds) Automata, Languages and Programming. ICALP 1979. Lecture Notes in Computer Science, vol 71. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-09510-1_39

Download citation

  • DOI: https://doi.org/10.1007/3-540-09510-1_39

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09510-1

  • Online ISBN: 978-3-540-35168-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation