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Structure and Complexity of Relational Queries
 Journal of Computer and System Sciences
, 1982
"... 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, i ..."
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Cited by 243 (3 self)
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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
TwoDimensional Languages
, 1997
"... this paper, much work have been done in studying properties of picture languages recognized by finitestate machines and several other models have been designed. A survey on this subject can be found in [21]. An intersting model of twodimensional tape acceptor is the twodimensional online tessell ..."
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Cited by 56 (3 self)
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this paper, much work have been done in studying properties of picture languages recognized by finitestate machines and several other models have been designed. A survey on this subject can be found in [21]. An intersting model of twodimensional tape acceptor is the twodimensional online tessellation automaton introduced by K. Inoue and A. Nakamura in [18]. This is defined as an infinite twodimensional array of identical conventional finitestate automata and it is a special type of cellular automaton. Despite it is not evident that it is a generalization of a onedimensional model, it can be easily 2 identified to a conventional automaton when restricted to onerow (or onecolumn) 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...
Logical characterizations of heap abstractions
, 2003
"... Abstract. 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 3valued firstorder logic. In ..."
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Cited by 30 (5 self)
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Abstract. 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 3valued firstorder logic. In that work, concrete stores are finite 2valued logical structures, and the sets of stores that can possibly arise during execution are represented (conservatively) using a certain family of finite 3valued logical structures. In this paper, we show how 3valued structures that arise in shape analysis can be characterized using formulas in firstorder logic with transitive closure. We also define a nonstandard (“supervaluational”) semantics for 3valued firstorder logic that is more precise than a conventional 3valued semantics, and demonstrate that it can be effectively implemented using existing theorem provers. 1
The Closure of Monadic NP
 Journal of Computer and System Sciences
, 1997
"... It is a wellknown result of Fagin that the complexity class NP coincides with the class of ..."
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Cited by 21 (0 self)
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It is a wellknown result of Fagin that the complexity class NP coincides with the class of
On the expression of graph properties in some fragments of monadic secondorder logic
 In Descriptive Complexity and Finite Models: Proceedings of a DIAMCS Workshop
, 1996
"... ABSTRACT: We review the expressibility of some basic graph properties in certain fragments of Monadic SecondOrder logic, like the set of MonadicNP 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 wher ..."
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Cited by 13 (1 self)
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ABSTRACT: We review the expressibility of some basic graph properties in certain fragments of Monadic SecondOrder logic, like the set of MonadicNP 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 3connected, and the other, logically simpler, uses the forbidden Kuratowski subgraphs.
Databases and FiniteModel Theory
 IN DESCRIPTIVE COMPLEXITY AND FINITE MODELS
, 1997
"... 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 finitemodel theorists, emphasizing the specificity of the database area. It is argued that the area of databases is a rich sourc ..."
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Cited by 6 (0 self)
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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 finitemodel 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 finitemodel theory.
A Probabilistic View of Datalog Parallelization
 Procs. Intl. Conf. on Database Theory
, 1993
"... We explore an approach to developing Datalog parallelization strategies that aims at good expected rather than worstcase 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 e ..."
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Cited by 4 (2 self)
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We explore an approach to developing Datalog parallelization strategies that aims at good expected rather than worstcase 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 01 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...
MSO Zero One Laws on Random Labelled Acyclic Graphs
 Discrete Math
"... Key words: random labelled trees, monadic second order zeroone laws, second order fraisseehrenfeucht games, second moment method PACS: 1 ..."
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Cited by 4 (2 self)
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Key words: random labelled trees, monadic second order zeroone laws, second order fraisseehrenfeucht games, second moment method PACS: 1
A Survey of Arithmetical Definability
, 2002
"... We survey definability and decidability issues related to firstorder fragments of arithmetic, with a special emphasis on Presburger and Skolem arithmetic and their (un)decidable extensions. ..."
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Cited by 2 (0 self)
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We survey definability and decidability issues related to firstorder fragments of arithmetic, with a special emphasis on Presburger and Skolem arithmetic and their (un)decidable extensions.
Random Trees
 J. Logic Comp
, 2000
"... 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, ..."
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Cited by 1 (1 self)
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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...