This paper is an attempt at laying the foundations for the classification of queries on relational data bases according to their structure and their computational complexity. Using the operations of composition and fixpoints, a Z--// hierarchy of height w 2, called the fixpoint query hierarchy, is defined, and its properties investigated. The hierarchy includes most of the queries considered in the literathre including those of Codd and Aho and Ullman

this paper, much work have been done in studying properties of picture languages recognized by finite-state machines and several other models have been designed. A survey on this subject can be found in [21]. An intersting model of two-dimensional tape acceptor is the two-dimensional on-line tessellation automaton introduced by K. Inoue and A. Nakamura in [18]. This is defined as an infinite two-dimensional array of identical conventional finite-state automata and it is a special type of cellular automaton. Despite it is not evident that it is a generalization of a one-dimensional model, it can be easily 2 identified to a conventional automaton when restricted to one-row (or one-column) pictures. Moreover, the family of picture languages recognized by this model of automaton satisfy many important properties. Different systems to generate pictures using grammars have been also explored (cf. [31, 32, 33, 35, 34, 36, 29, 30, 39]). However, in the finite state case, this approach is shown to be less powerful than others. Another possible generalization is to describe picture languages by logic formulas. Recently, W. Thomas gave a general formalism to describe graphs (and, in particular, pictures) as model theoretical structures and showed as "recognizability" corresponds to the notions of definability on existential monadic second order logic (cf. [38]). This is coherent with the string language recognizability theory where Buchi's Theorem holds. In a recent proposal (cf. [13, 14]) a notion of recognizability of a set of pictures in terms of tiling systems is introduced. The underlying idea is to define recognizability by "projection of local properties". Informally, recognition in a tiling system is defined in terms of a finite set of square pictures of side two which c...

It is a well-known result of Fagin that the complexity class NP coincides with the class of

ABSTRACT: We review the expressibility of some basic graph properties in certain fragments of Monadic Second-Order logic, like the set of Monadic-NP formulas. We focus on cases where a property and its negation are both expressible in the same (or in closely related) fragments. We examine cases where edge quantifications can be eliminated and cases where they cannot. We compare two logical expressions of planarity: one of them is constructive in the sense that it defines a planar embedding of the considered graph if it is planar and 3-connected, and the other, logically simpler, uses the forbidden Kuratowski subgraphs.

Databases provide one of the main concrete scenarios for finitemodel theory within computer science. This paper presents an informal overview of database theory aimed at finite-model theorists, emphasizing the specificity of the database area. It is argued that the area of databases is a rich source of questions and vitality for finite-model theory.

We explore an approach to developing Datalog parallelization strategies that aims at good expected rather than worst-case performance. To illustrate, we consider a very simple parallelization strategy that applies to all Datalog programs. We prove that this has very good expected performance under equal distribution of inputs. This is done using an extension of 0-1 laws adapted to this context. The analysis is confirmed by experimental results on randomly generated data. 1 Introduction The performance requirements of databases for advanced applications, and the increased availability of cheap parallel processing, have naturally lend great importance to the development of parallel processing techniques for databases. Much of the existing research in this direction has focused on parallelization of Datalog queries. In this paper we investigate parallel processing of Datalog from a probabilistic viewpoint. In contrast to existing work, we propose to guide the design and evaluation of para...

Key words: random labelled trees, monadic second order zero-one laws, second order fraisse-ehrenfeucht games, second moment method PACS: 1

We survey de nability and decidability issues related to rst-order fragments of arithmetic, with a special emphasis on Presburger and Skolem arithmetic and their (un)decidable extensions.

We briefly review a small fraction of the literature for anyone interested in random trees in logic, linguistics, or computer science. This note should be regarded as a sort of disorganized bibliography for anyone who is interested in pursuing the subject. One way to study languages, algorithms, and similar mechanical constructions is to choose some inputs at random, feed them into the machine, and see what happens. We can do this theoretically as follows: suppose that each input is either ACCEPTED or REJECTED. Since we are often interested in quite large inputs, we might ask: Question 1 For each n, let I n be the set of all inputs of size n. 1. Given a machine M , what is the probability p n that a randomly chosen input from I n is accepted? 2. What happens to p n as n gets large? Question 1(1), "what is p n ?" is often a quite difficult problem in "enumerative combinatorics. " On the other hand, Question 1(2), "what happens to p n as n !1?" is often tractible. The answer to t...

Shape analysis concerns the problem of determining “shape invariants ” for programs that perform destructive updating on dynamically allocated storage. In recent work, we have shown how shape analysis can be performed using an abstract interpretation based on three-valued first-order logic. In that work, concrete stores are finite two-valued logical structures, and the sets of stores that can possibly arise during execution are represented (conservatively) using a certain family of finite three-valued logical structures. In this article, we show how three-valued structures that arise in shape analysis can be characterized using formulas in first-order logic with transitive closure. We also define a nonstandard (“supervaluational”) semantics for three-valued first-order logic that is more precise than a conventional three-valued semantics, and demonstrate that the supervaluational semantics can be implemented using existing theorem provers.