Optimal parallel parsing of bracket languages

  • Wojciech Rytter
  • Raffaele Giancarlo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 269)


We prove that the parsing problem for bracket context-free languages can be solved in log(n) time using n/log(n) processors on a parallel random access machine without write conflicts (P-RAM). On the way we develop a new technique for tree compression based on the bracket structure of the tree. It is especially useful when a function is to be computed for all nodes of the tree, because the decompression is easy, while the technique from [2] is best suited for computing the value associated only with the root.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    I. Bar-On, and U. Vishkin., Optimal parallel generation of a computation tree form. ACM Trans.on Progr.Lang.and Systems 7:2 (1985),348–357CrossRefGoogle Scholar
  2. [2]
    A.Gibbons, W.Rytter. An optimal parallel algorithm for dynamic expression evaluation and its applications. accepted for Found.of Software Techn.and Theoretical Comp.Science,december (1986), to appear in Lect.Notes in Comp.Science,Springer-Verlag.Google Scholar
  3. [3]
    Fortune,S. and Wyllie,J. Parallelism in random access machines, Proceedings of the 10th ACM Symp. Theory of Comp.(1978) 114–118.Google Scholar
  4. [4]
    G. Kindervater,J. Lenstra. An introduction to parallelism in combinatorial optimization. Report OS-R8501, Centre for Math.and Comp.Science, Amsterdam (1984)Google Scholar
  5. [5]
    R.Mattheyses, and C.M.Fiduccia, Parsing Dyck languages on parallel machines. 20th Allerton Conference on Comm.Control and Computing (1982)Google Scholar
  6. [6]
    K. Mehlhorn. Bracket languages are recognizable in logarithmic space. Inf.Proc.Letters 5:6 (1976) 169–170Google Scholar
  7. [7]
    W. Ruzzo. On the complexity of general context free language parsing and recognition. Automata, languages and programming. Lect.Notes in Computer Science (1979),pp.489–499Google Scholar
  8. [8]
    W.Rytter. On the complexity of parallel parsing of general context-free languages. Accepted for Theoretical Computer ScienceGoogle Scholar
  9. [9]
    W. Rytter. On the recognition of context free languages. Computation Theory, Lect.Notes in Comp.Science 208,Springer Verlag (1985),pp.318–325Google Scholar
  10. [10]
    W. Rytter. An application of Mehlhorn algorithm for bracket languages to log n space recognition of input driven languages. Inf.Processing Letters,23:2 (1986) 81–84MathSciNetGoogle Scholar
  11. [11]
    W.Rytter. The complexity of two-way pushdown automata and recursive programs. in Combinatorial algorithms on words (ed.A.Apostolico,Z.Galil), Springer-Verlag (1985) 341–356Google Scholar
  12. [12]
    W. Rytter. Parallel time log n recognition of unambiguous cfl's. Fund.of Computation Theory, Lect.Notes in Computer Science 199 (1985) 380–389,full version to appear in Inf. and ControlGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Wojciech Rytter
    • 1
    • 2
  • Raffaele Giancarlo
    • 3
    • 4
  1. 1.Dept.of Computer ScienceUniversity of WarwickCoventryEngland
  2. 2.Institute of InformaticsWarsaw UniversityPoland
  3. 3.Dept.of InformaticsUniversity of SalernoItaly
  4. 4.Dept. of Computer ScienceColumbia UniversityNew YorkUSA

Personalised recommendations