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Parallel recognition and ranking of context-free languages

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Mathematical Foundations of Computer Science 1992 (MFCS 1992)

Part of the book series: Lecture Notes in Computer Science ((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.

The work of the first two authors was supported by the Deutsche Forschungsgemeinschaft, SFB 342, TP A4: “KLARA”. The work of the third author was supported by the grant KBN 2-1190-91-01 of the Polish Ministery of Education.

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Authors and Affiliations

  1. Institut Für Informatik, Technische Universität München, Germany

    Klaus-Jörn Lange & Peter Rossmanith

  2. Institute of Informatics, Warsaw University, ul.Banacha 2, 02-097, Warszawa, Poland

    Wojciech Rytter

Authors
  1. Klaus-Jörn Lange
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  2. Peter Rossmanith
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  3. Wojciech Rytter
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Ivan M. Havel Václav Koubek

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© 1992 Springer-Verlag Berlin Heidelberg

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Lange, KJ., Rossmanith, P., Rytter, W. (1992). Parallel recognition and ranking of context-free languages. In: Havel, I.M., Koubek, V. (eds) Mathematical Foundations of Computer Science 1992. MFCS 1992. Lecture Notes in Computer Science, vol 629. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-55808-X_3

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  • DOI: https://doi.org/10.1007/3-540-55808-X_3

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  • Print ISBN: 978-3-540-55808-8

  • Online ISBN: 978-3-540-47291-9

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