Bibliography | Kufleitner, Manfred; Lauser, Alexander: Around Dot-depth One. University of Stuttgart, Faculty of Computer Science, Electrical Engineering, and Information Technology, Technical Report Computer Science No. 2011/03. 15 pages, german.
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CR-Schema | F.4.1 (Mathematical Logic) F.4.3 (Formal Languages)
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Keywords | finite semigroups; dot-depth; regular languages; first-order logic |
Abstract | The dot-depth hierarchy is a classification of star-free languages. It is related to the quantifier alternation hierarchy of first-order logic over finite words. We consider fragments of languages with dot-depth 1/2 and dot-depth 1 obtained by prohibiting the specification of prefixes or suffixes. As it turns out, these language classes are in one-to-one correspondence with fragments of existential first-order logic without min- or max-predicate. For all fragments, we obtain effective algebraic characterizations. Moreover, we give new combinatorial proofs for the decidability of the membership problem for dot-depth 1/2 and dot-depth 1.
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Full text and other links | PDF (494995 Bytes) PostScript (924488 Bytes)
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Department(s) | University of Stuttgart, Institute of Formal Methods in Computer Science, Theoretical Computer Science
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Entry date | March 8, 2011 |
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