Bad news on decision problems for patterns
journal contributionposted on 2008-10-01, 13:57 authored by Dominik FreydenbergerDominik Freydenberger, Daniel Reidenbach
We study the inclusion problem for pattern languages, which is shown to be undecidable by Jiang et al. (J. Comput. System Sci. 50, 1995). More precisely, Jiang et al. demonstrate that there is no effective procedure deciding the inclusion for the class of all pattern languages over all alphabets. Most applications of pattern languages, however, consider classes over fixed alphabets, and therefore it is practically more relevant to ask for the existence of alphabet-specific decision procedures. Our first main result states that, for all but very particular cases, this version of the inclusion problem is also undecidable. The second main part of our paper disproves the prevalent conjecture on the inclusion of so-called similar E-pattern languages, and it explains the devastating consequences of this result for the intensive previous research on the most prominent open decision problem for pattern languages, namely the equivalence problem for general E-pattern languages.
- Computer Science
CitationFREYDENBERGER, D.D. and REIDENBACH, D., 2008. Bad news on decision problems for patterns. Lecture Notes in Computer Science, 5257, pp. 327-338.
Publisher© Springer Verlag
NotesThis is a journal article. It was published in Lecture Notes in Computer Science [© Springer Verlag] and the definitive version is available at: www.springerlink.com