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Computing the Longest Common Prefix of a Context-free Language in Polynomial Time
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35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
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- Publication Date: 2018-02-27
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Michael Luttenberger, Raphaela Palenta, and Helmut Seidl. Computing the Longest Common Prefix of a Context-free Language in Polynomial Time. In 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, pp. 48:1-48:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.STACS.2018.48
Abstract
We present two structural results concerning the longest common prefixes of non-empty languages. First, we show that the longest common prefix of the language generated by a context-free grammar of size N equals the longest common prefix of the same grammar where the heights of the derivation trees are bounded by 4N. Second, we show that each non-empty language L has a representative subset of at most three elements which behaves like L w.r.t. the longest common prefix as well as w.r.t. longest common prefixes of L after unions or concatenations with arbitrary other languages. From that, we conclude that the longest common prefix, and thus the longest common suffix, of a context-free language can be computed in polynomial time.
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- longest common prefix
- context-free languages
- combinatorics on words
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References
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