6,166 research outputs found

    Logics for Unranked Trees: An Overview

    Get PDF
    Labeled unranked trees are used as a model of XML documents, and logical languages for them have been studied actively over the past several years. Such logics have different purposes: some are better suited for extracting data, some for expressing navigational properties, and some make it easy to relate complex properties of trees to the existence of tree automata for those properties. Furthermore, logics differ significantly in their model-checking properties, their automata models, and their behavior on ordered and unordered trees. In this paper we present a survey of logics for unranked trees

    Deciding the Borel complexity of regular tree languages

    Full text link
    We show that it is decidable whether a given a regular tree language belongs to the class Δ20{\bf \Delta^0_2} of the Borel hierarchy, or equivalently whether the Wadge degree of a regular tree language is countable.Comment: 15 pages, 2 figure

    An Upper Bound on the Complexity of Recognizable Tree Languages

    Get PDF
    The third author noticed in his 1992 PhD Thesis [Sim92] that every regular tree language of infinite trees is in a class (D_n(Σ0_2))\Game (D\_n({\bf\Sigma}^0\_2)) for some natural number n1n\geq 1, where \Game is the game quantifier. We first give a detailed exposition of this result. Next, using an embedding of the Wadge hierarchy of non self-dual Borel subsets of the Cantor space 2ω2^\omega into the class Δ1_2{\bf\Delta}^1\_2, and the notions of Wadge degree and Veblen function, we argue that this upper bound on the topological complexity of regular tree languages is much better than the usual Δ1_2{\bf\Delta}^1\_2

    Fragments of first-order logic over infinite words

    Get PDF
    We give topological and algebraic characterizations as well as language theoretic descriptions of the following subclasses of first-order logic FO[<] for omega-languages: Sigma_2, FO^2, the intersection of FO^2 and Sigma_2, and Delta_2 (and by duality Pi_2 and the intersection of FO^2 and Pi_2). 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.Comment: Conference version presented at 26th International Symposium on Theoretical Aspects of Computer Science, STACS 200

    Languages of Dot-depth One over Infinite Words

    Full text link
    Over finite words, languages of dot-depth one are expressively complete for alternation-free first-order logic. This fragment is also known as the Boolean closure of existential first-order logic. Here, the atomic formulas comprise order, successor, minimum, and maximum predicates. Knast (1983) has shown that it is decidable whether a language has dot-depth one. We extend Knast's result to infinite words. In particular, we describe the class of languages definable in alternation-free first-order logic over infinite words, and we give an effective characterization of this fragment. This characterization has two components. The first component is identical to Knast's algebraic property for finite words and the second component is a topological property, namely being a Boolean combination of Cantor sets. As an intermediate step we consider finite and infinite words simultaneously. We then obtain the results for infinite words as well as for finite words as special cases. In particular, we give a new proof of Knast's Theorem on languages of dot-depth one over finite words.Comment: Presented at LICS 201
    corecore