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(n 2) processors in time O(log2 n).
The work of this author was partly done during his stay at the University of Paderborn and was supported by the German Research Association (DFG)
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© 1990 Springer-Verlag Berlin Heidelberg
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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. https://doi.org/10.1007/3-540-52282-4_33
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DOI: https://doi.org/10.1007/3-540-52282-4_33
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