Skip to main content
SpringerLink
Log in

An NC algorithm for recognizing tree adjoining languages

  • Published:
International Journal of Parallel Programming Aims and scope Submit manuscript

Abstract

A parallel algorithm is presented for recognizing the class of languages generated by tree adjoining grammars, a tree rewriting system which has applications in natural language processing. This class of languages is known to properly include all context-free languages; for example, the noncontext-free sets {a n b n c n} and {ww} are in this class. It is shown that the recognition problem for tree adjoining languages can be solved by a concurrent read, concurrent write parallel random-access machine (CRCW PRAM) inO(logn) time using polynomially many processors. Thus, the class of tree adjoining languages is inAC 1 and hence inNC. This extends a previous result for context-free languages.

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. A. K. Joshi, L. S. Levy, and M. Takahashi, Tree Adjunct Grammars,J. Comput. and Syst. Sci. 10:136–163 (1975).

    Google Scholar 

  2. A. K. Joshi, How Much Context-Sensitivity is Necessary for Characterizing Structural Descriptions—Tree Adjoining Grammars,Natural Language Processing—Theoretical, Computational and Psychological Perspectives, D. Dowty, L. Karttunen, and A. Zwicky (eds.), Cambridge University Press, New York (1985).

    Google Scholar 

  3. A. S. Kroch and A. K. Joshi, The Linguistic Relevance of Tree Adjoining Grammar, Tech. Rep. MS-CIS-85-16, Department of Computer and Information Science, University of Pennsylvania (June 1985).

  4. A. Abeillé, Parsing French with Tree Adjoining Grammar: Some Linguistic Accounts,Proc. 12th Int. Conf. on Computational Linguistics, Budapest (August 1988).

  5. A. Abeillé, A Lexicalized Tree Adjoining Grammar for French: The General Framework, Tech. Rep. MS-CIS-88-64, Department of Computer and Information Science, University of Pennsylvania (1988).

  6. A. Abeillé, Extraction Out of NP in Tree Adjoining Grammars,The 24th Regional Meeting of the Chicago Linguistic Society, Chicago, Illinois (1988).

  7. A. Abeillé and Y. Schabes, Parsing Idioms in Tree Adjoining Grammars,Proc. Fourth Conf. of the European Chapter of the Assoc. for Computational Linguistics, Manchester (1989).

  8. K. Bishop, S. Cote, and A. Abeillé, A Lexicalized Tree Adjoining Grammar for English, Tech. Rep., Department of Computer and Information Science, University of Pennsylvania (1989).

  9. A. Abeillé, K. Bishop, S. Cote Y. Schabes, and A. K. Joshi, Parsing with Tree Adjoining Grammars: The Current State of Implementation, Tech. Rep., Department of Computer and Information Science, University of Pennsylvania (August 1988).

  10. K. Vijayashanker and A. K. Joshi, Some Computational Properties of Tree Adjoining Grammars,Proc. of the 23rd Ann. Meeting of the Assoc. for Computational Linguistics Chicago, Illinois, pp. 82–93 (July 1985).

  11. D. J. Weir, From Context-Free Grammars to Tree Adjoining Grammars and Beyond, Tech. Rep. MS-CIS-87-42, Department of Computer and Information Science, University of Pennsylvania (May 1987).

  12. S. R. Kosaraju, Speed of Recognition of Context-Free Languages by Array Automata,SIAM Journal on Computing 4(3):331–340 (1975).

    Google Scholar 

  13. Y. Chiang and K. S. Fu, Parallel Parsing and VLSI Implementations for Syntactic Pattern Recognition,IEEE Trans. PAMI 6(3):302–313 (1984).

    Google Scholar 

  14. J. H. Chang, O. H. Ibarra, and M. A. Palis, Parallel Parsing on a One-Way Array of Finite-State Machines,IEEE Trans. on Comput. C-36(1):64–75 (January 1987).

    Google Scholar 

  15. L. Langlois, Parallel Parsing of Context-Free Languages on an Array of Processors, PhD Thesis, University of Edinburgh (September 1988).

  16. W. L. Ruzzo, Tree-size Bounded Alternation,J. of Comput. and Syst. Sci. 21:218–235.

  17. L. Stockmeyer and U. Vishkin, Simulation of Parallel Random Access Machines by Circuits,SIAM Journal on Computing 13:409–422 (1984).

    Google Scholar 

  18. S. A. Cook, A Taxonomy of Problems with Fast Parallel Algorithms,Infor. and Contr. 64:2–22 (1985).

    Google Scholar 

  19. W. Rytter, The Complexity of Two-Way Pushdown Automata and Recursive Programs,Combinatorial Algorithms on Words, A. Apostolico and Z. Galil (eds.), NATO ASI Series F: 12, Springer-Verlag, New York/Berlin.

  20. J. Reif, ParallelO(logn) Time Acceptance of Deterministic CFLs,Proc. 23rd IEEE Symp. on Foundations of Comput. Sci., pp. 290–296 (1982).

  21. W. Rytter, ParallelO(logn) Recognition of Unambiguous Context-Free Languages,Infor. and Comput. 73:75–86 (1987).

    Google Scholar 

  22. A. V. Aho and J. D. Ullman,Theory of Parsing, Translation and Compiling, Volume 1: Parsing, Prentice-Hall, Englewood Cliffs, New Jersey (1972).

    Google Scholar 

  23. C. N. Fischer, On Parsing Context-Free Languages in Parallel Environments, PhD Thesis, Cornell University (1975).

  24. C. N. Fischer, On Parsing and Compiling Arithmetic Expressions on Vector Computers,ACM Trans. PAS 2(2):203–224 (April 1980).

    Google Scholar 

  25. R. M. Schell, Methods for Constructing Parallel Compilers for Use in a Multiprocessor Environment, PhD Thesis, University of Illinois at Urbana-Champaign (1979).

  26. J. Cohen, T. Hickey, and J. Katcoff, Upper-Bounds for Speed-Up in Parallel Parsing,J. of the ACM 29(2):408–428 (1982).

    Google Scholar 

  27. J. Cohen and S. Kolonder, Estimating the Speed-Up in Parallel Parsing,IEEE Trans. on Software Engineering 11(1):114–124 (January 1985).

    Google Scholar 

  28. D. B. Skillicorn and D. T. Barnard, Parallel Parsing on the Connection Machine,Infor. Proc. Lett. 31(3):111–117 (May 1989).

    Google Scholar 

  29. M. A. Palis, S. M. Shende, and D. S. L. Wei, An Optimal Linear-Time Parallel Parser for Tree Adjoining Languages,SIAM Journal on Computing 19(1):1–31 (February 1990).

    Google Scholar 

  30. M. A. Palis and S. M. Shende, Upper Bounds on Recognition of a Hierarchy of Noncontext-Free Languages,Theoret. Comput. Sci. 98:289–319 (1992).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, New Jersey Institute of Technology, 07102, Newark, New Jersey

    Michael A. Palis

  2. Department of Computer Science and Engineering, University of Nebraska at Lincoln, 68588, Lincoln, Nebraska

    Sunil M. Shende

Authors
  1. Michael A. Palis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sunil M. Shende
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research was supported in part by NSF Grants IRI 92-96249, MCS 82-19116-CER, MCS 82-07294, DCR 84-10413, MCS 83-05221, ARO Grant DAA29-84-9-0027, DARPA Grant N00014-85-K-0018, and by the New Jersey Institute of Technology under Grant Nos. 421690 and 211665.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Palis, M.A., Shende, S.M. An NC algorithm for recognizing tree adjoining languages. Int J Parallel Prog 21, 151–167 (1992). https://doi.org/10.1007/BF01408291

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01408291

Key Words

Search

Navigation