Caterpillars and context-free languages

  • Michal P. Chytil
  • Burkhard Monien
Conference paper

DOI: 10.1007/3-540-52282-4_33

Part of the Lecture Notes in Computer Science book series (LNCS, volume 415)
Cite this paper as:
Chytil M.P., Monien B. (1990) Caterpillars and context-free languages. In: Choffrut C., Lengauer T. (eds) STACS 90. STACS 1990. Lecture Notes in Computer Science, vol 415. Springer, Berlin, Heidelberg

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).

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

Personalised recommendations