Optimal time bounds for parallel term matching

  • Rakesh M. Verma
  • I. V. Ramakrishnan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 310)


Term Matching is a fundamental operation in term rewriting, functional programming and logic programming. Parallel algorithms for this operation have attracted much attention recently. However nontrivial lower bounds for term matching are as yet unknown. In this paper, we obtain lower bounds on parallel time for this problem. We also establish the tightness of our lower bounds for some representations and several models, by giving matching upper bounds with as few processors as possible.

Key words and phrases

complexity optimal bounds parallel term matching 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Paul Beame and John Hastad, Optimal bounds for decision problems on the CRCW PRAM, In Proceedings of the ACM Symposium on Theory of Computing, pages 83–93, 1987.Google Scholar
  2. [2]
    Ashok K. Chandra, L. Stockmeyer, and U. Vishkin, Constant depth reducibility, SIAM Journal of Computing, 13:423–439 (1984).CrossRefGoogle Scholar
  3. [3]
    Richard Cole and Uzi Vishkin, Approximate and exact parallel scheduling with applications to list, tree and graph problems, In Proceedings of the IEEE Conference on Foundations of Computer Science, pages 478–491, 1986.Google Scholar
  4. [4]
    Stephen Cook and Cynthia Dwork, Bounds on the time for parallel RAM's to compute simple functions, In Proceedings of the ACM Symposium on Theory of Computing, pages 231–233, 1982.Google Scholar
  5. [5]
    C. Dwork, P. Kanellakis, and J.C. Mitchell, On the sequential nature of unification, Journal of Logic Programming, 1:35–50 (1984).CrossRefGoogle Scholar
  6. [6]
    C. Dwork, P. Kanellakis, and L. Stockmeyer, Parallel algorithms for term matching, In Eighth CADE, Springer-Verlag LNCS vol. 230, 1986.Google Scholar
  7. [7]
    Steven Fortune and James Wyllie, Parallelism in random access machines, In Proceedings of the ACM Symposium on Theory of Computing, pages 114–118, 1978.Google Scholar
  8. [8]
    C.P. Kruskal, L. Rudolph, and M. Snir, Efficient parallel algorithms for graph problems, In Proceedings of International Conference on Parallel Processing, pages 180–185, 1985.Google Scholar
  9. [9]
    R. Ramesh and I.V. Ramakrishnan, Optimal speedups for parallel pattern matching in trees, In Second RTA, Springer-Verlag LNCS vol. 256, 1987.Google Scholar
  10. [10]
    R. Ramesh, R.M. Verma, T. Krishanprasad, and I.V. Ramakrishnan, Term matching on parallel computers, In Fourteenth ICALP, Springer-Verlag LNCS vol. 267, 1987.Google Scholar
  11. [11]
    Y. Shiloach and U. Vishkin, Finding the maximum, merging and sorting in a parallel computation model, Journal of Algorithms, 2:88–102 (1981).CrossRefGoogle Scholar
  12. [12]
    Rakesh M. Verma, T. Krishnaprasad, and I. V. Ramakrishnan, An efficient parallel algorithm for Term Matching, In Sixth FST-TCS, Springer-Verlag LNCS vol. 241, 1986.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Rakesh M. Verma
    • 1
  • I. V. Ramakrishnan
    • 1
  1. 1.Department of Computer ScienceState University of New York at Stony BrookStony Brook

Personalised recommendations