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Parallel recognition and ranking of context-free languages

  • Klaus-Jörn Lange
  • Peter Rossmanith
  • Wojciech Rytter
Invited Lectures
Part of the Lecture Notes in Computer Science book series (LNCS, volume 629)

Abstract

We survey the efficiency of the ‘fast’ parallel algorithms for the recognition and ranking of context-free languages on the Parallel Random Access Machine without write conflicts. The efficiency of the algorithm is the total number of operations (the product of time and number of processors). Such efficiency depends heavily on the class of context-free grammars and on the meaning of ‘fast’: log(n), log2n or sublinear time. The slower is the algorithm the better is its total efficiency. Several new results are presented in the paper. A new simpler version of the log(n) time parallel recognition of unambiguous cfl's is presented. The parallel complexity of ranking and max-word problems for several classes of cfl's is related to the complexity of certain (⊕,⊗)-transitive closure problems, where (⊕,⊗)=(+,*) for the ranking problem of unambiguous languages and (⊕,⊗)=(max,concat) for the max-word problem. This simplifies the ranking and max-word algorithms and reduces the number of processors.

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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Klaus-Jörn Lange
    • 1
  • Peter Rossmanith
    • 1
  • Wojciech Rytter
    • 2
  1. 1.Institut Für InformatikTechnische Universität MünchenGermany
  2. 2.Institute of InformaticsWarsaw UniversityWarszawaPoland

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