05 Fakultät Informatik, Elektrotechnik und Informationstechnik

Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/6

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Publication Type: search.filters.UBSTyp.ArbeitspapierAuthor: search.filters.author.Diekert, Volker

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Now showing 1 - 4 of 4
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    Fragments of first-order logic over infinite words
    (2009) Diekert, Volker; Kufleitner, Manfred
    We give topological and algebraic characterizations as well as language theoretic descriptions of the following subclasses of first-order logic for omega-languages: Sigma2, FO2, the intersection of FO2 and Sigma2, and Delta2 (and by duality Pi2 and the intersection of FO2 and Pi2). These descriptions extend the respective results for finite words. In particular, we relate the above fragments to language classes of certain (unambiguous) polynomials. An immediate consequence is the decidability of the membership problem of these classes, but this was shown before by Wilke and Bojanczyk and is therefore not our main focus. The paper is about the interplay of algebraic, topological, and language theoretic properties.
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    Existential and positive theories of equations in graph products
    (2001) Diekert, Volker; Lohrey, Markus
    We prove that the existential theory of equations with normalized rational constraints in a fixed graph product of finite monoids, free monoids, and free groups is PSPACE-complete. Under certain restrictions this result also holds if the graph product is part of the input. As the second main result we prove that the positive theory of equations with recognizable constraints in graph products of finite and free groups is decidable.
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    Makanin's algorithm for solving word equations with regular constraints
    (1998) Diekert, Volker
    We give a self-contained proof of a fundamental result of Makanin (1977), which solves the satisfiability problem of equations with constants over free monoids. Our presentation of Makanin's algorithm is borrows Schulz (1992a), where Makanin's result is extended to the case where solutions are restricted by imposing regular constraints on the variables. This report appears (with minor modifications) as a chapter of the new book of M. Lothaire Algebraic Combinatorics on Words.
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    Complexity results and the growths of hairpin completions of regular languages
    (2010) Diekert, Volker; Kopecki, Steffen
    The hairpin completion is a natural operation on formal languages which has been inspired by molecular phenomena in biology and by DNA-computing. In 2009 we presented a (polynomial time) decision algorithm to decide regularity of the hairpin completion. In this paper we provide four new results: 1.) We show that the decision problem is NL-complete. 2.) There is a polynomial time decision algorithm which runs in time O(n8), this improves our previous results, which provided O(n^{20}). 3.) For the one-sided case (which is closer to DNA computing) the time is O(n2), only. 4.) The hairpin completion of a regular language is unambiguous linear context-free. This result allows to compute the growth (generating function) of the hairpin completion and to compare it with the growth of the underlying regular language.