Caterpillars and context-free languages
- 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
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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