this paper are (i) a construction by which, for a given bounded treewidth, a general MS graph property P is transformed to an MS binary tree property r(P), and a general labeled graph G with a suitable tree-decomposition is transformed to a labeled binary tree T(G) in time linear in the number of vertices of G and in such a way that P holds for G if and only if r(P) holds for T(G). This allows us, using techniques developed by Doner [20] and Thatcher and Wright [42], to compile a tree automaton which decides the MS-problem r(P) on the tree T(G) (and thus also P on the graph G) in linear time, and (ii) a procedure whereby such an automaton for a MS formula with free variables is modified to solve a related EMS problem involving counting

There is a significant amount of interest in combining and extending database and information retrieval technologies to manage textual data. The challenge is becoming more relevant due to increased availability of documents in digital form. Document data has a natural hierarchical structure, which may be made explicit due to the use of mark-up conventions (as with SGML). An important aspect of managing structured and semi-structured textual data consists of supporting the efficient retrieval of text components based both on their content and structure. In this paper we study issues related to the expressive power and optimization of a class of algebras that support combining string (or pattern) searches with queries on the hierarchical structure of the text. The region algebra studied is a set-at-a-time algebra for manipulating text regions (substrings of the text) that supports finding out nesting and ordering properties of the text regions. This algebra is part of the language in us...

We show that the first-order theory of structural subtyping of non-recursive types is decidable, as a consequence of a more general result on the decidability of term powers of decidable theories.

. The first-order theories of finite and rational, constructor and feature trees possess complete axiomatizations and are decidable by quantifier elimination [15, 13, 14, 5, 10, 3, 20, 4, 2]. By using the uniform inseparability lower bounds techniques due to Compton and Henson [6], based on representing large binary relations by means of short formulas manipulating with high trees, we prove that all the above theories, as well as all their subtheories, are non-elementary in the sense of Kalmar, i.e., cannot be decided within time bounded by a k- story exponential function 1 exp k (n) for any fixed k. Moreover, for some constant d ? 0 these decision problems require nondeterministic time exceeding exp 1 (bdnc) infinitely often. 1 Introduction Trees are fundamental in Computer Science. Different tree structures are used as underlying domains in automated theorem proving, term rewriting, functional and logic programming, constraint solving, symbolic computation, knowledge re...

this article is a proof that each FO problem can be solved in linear time if only relational structures of bounded degree are considered. The basic idea of the proof is a localization technique based on a method that was originally developed by Hanf (Hanf 1965) to show that the elementary theories of two structures are equal under certain conditions, i.e., that two structures agree on all first-order sentences. Fagin, Stockmeyer and Vardi (Fagin et al. 1993) developed a variant of this technique, which is applicable in descriptive complexity theory to classes of finite relational structures of uniformly bounded degree. Variants of this result can also be found in Gaifman (1982) (see also Thomas (1991)). The essential content of this result, which is also called the Hanf-Sphere Lemma, is that two relational structures of bounded degree satisfy the same first-order sentences of a certain quantifier-rank if both contain, up to a certain number m, the same number of isomorphism types of substructures of a bounded radius r. In addition, a technique of model interpretability from Rabin (1965) (see also Arnborg et al. (1991), Seese (1992), Compton and Henson (1987) and Baudisch et al. (1982)) is adapted to descriptive complexity classes, and proved to be useful for reducing the case of an arbitrary class of relational structures to a class of structures consisting only of the domain and one binary irreflexive and symmetric relation, i.e., the class of simple graphs. It is shown that the class of simple graphs is lintime-universal with respect to first-order logic, which shows that many problems on descriptive complexity classes, described in languages extending first-order logic for arbitrary structures, can be reduced to problems on simple graphs. This paper is organized as f...

In software verification it is often required to prove statements about heterogeneous domains containing elements of various sorts, such as counters, stacks, lists, trees and queues. Any

Abstract not found

We present a technique that enables the use of finite model finding to check the satisfiability of certain formulas whose intended models are infinite. Such formulas arise when using the language of sets and relations to reason about structured values such as algebraic datatypes. The key idea of our technique is to identify a natural syntactic class of formulas in relational logic for which reasoning about infinite structures can be reduced to reasoning about finite structures. As a result, when a formula belongs to this class, we can use existing finite model finding tools to check whether the formula holds in the desired infinite model. 1

Besides the very successful concept of tree-width (see [Bodlaender, H. and Koster, A. (2007) Combinatorial optimisation on graphs of bounded treewidth. These are special issues on Parameterized Complexity]), many concepts and parameters measuring the similarity or dissimilarity of structures compared to trees have been born and studied over the past years. These concepts and parameters have proved to be useful tools in many applications, especially in the design of efficient algorithms. Our presented novel look at the contemporary developments of these ‘width ’ parameters in combinatorial structures delivers—besides traditional tree-width and derived dynamic programming schemes—also a number of other useful parameters like branch-width, rank-width (clique-width) or hypertree-width. In this contribution, we demonstrate how ‘width ’ parameters of graphs and generalized structures (such as matroids or hypergraphs), can be used to improve the design of parameterized algorithms and the structural analysis in other applications on an abstract level.

.)L: TA! Z. Formulae are formed from term literals and integerliterals using logical connectives and quantifications. Term literals are exactly