Caterpillars and context-free languages

  • Michal P. Chytil
  • Burkhard Monien
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 415)

Abstract

We use the concept of a caterpillar tree to study the properties of context-free languages, in particular new results about the index of context-free languages and the recognition of context-free languages are obtained this way. The first group of results points to differences between ambiguous and unambiguous languages. For unambiguous languages we prove the existence of a gap between finite index and O(log n) index. For ambiguous languages there is no such a gap: we prove the existence of grammars with infinite but arbitrarily slowly growing index. We show that bounded languages are of finite index and give a deterministic log space algorithm for the recognition of deterministic finite index languages. We also describe a parallel algorithm recognizing deterministic context-free languages on a CREW-PRAM with O(n2) processors in time O(log2n).

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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Michal P. Chytil
    • 1
  • Burkhard Monien
    • 2
  1. 1.Charles UniversityPraha 1
  2. 2.Math. and Computer ScienceUniversity of PaderbornPaderborn

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