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118
Compositional Model Checking
, 1999
"... We describe a method for reducing the complexity of temporal logic model checking in systems composed of many parallel processes. The goal is to check properties of the components of a system and then deduce global properties from these local properties. The main difficulty with this type of approac ..."
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Cited by 2426 (62 self)
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We describe a method for reducing the complexity of temporal logic model checking in systems composed of many parallel processes. The goal is to check properties of the components of a system and then deduce global properties from these local properties. The main difficulty with this type of approach is that local properties are often not preserved at the global level. We present a general framework for using additional interface processes to model the environment for a component. These interface processes are typically much simpler than the full environment of the component. By composing a component with its interface processes and then checking properties of this composition, we can guarantee that these properties will be preserved at the global level. We give two example compositional systems based on the logic CTL*.
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 244 (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
Fresh Logic
 Journal of Applied Logic
, 2007
"... Abstract. The practice of firstorder logic is replete with metalevel concepts. Most notably there are metavariables ranging over formulae, variables, and terms, and properties of syntax such as alphaequivalence, captureavoiding substitution and assumptions about freshness of variables with resp ..."
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Cited by 186 (21 self)
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Abstract. The practice of firstorder logic is replete with metalevel concepts. Most notably there are metavariables ranging over formulae, variables, and terms, and properties of syntax such as alphaequivalence, captureavoiding substitution and assumptions about freshness of variables with respect to metavariables. We present oneandahalfthorder logic, in which these concepts are made explicit. We exhibit both sequent and algebraic specifications of oneandahalfthorder logic derivability, show them equivalent, show that the derivations satisfy cutelimination, and prove correctness of an interpretation of firstorder logic within it. We discuss the technicalities in a wider context as a casestudy for nominal algebra, as a logic in its own right, as an algebraisation of logic, as an example of how other systems might be treated, and also as a theoretical foundation
Logic and the Challenge of Computer Science
, 1988
"... Nowadays computer science is surpassing mathematics as the primary field of logic applications, but logic is not tuned properly to the new role. In particular, classical logic is preoccupied mostly with infinite static structures whereas many objects of interest in computer science are dynamic objec ..."
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Cited by 153 (16 self)
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Nowadays computer science is surpassing mathematics as the primary field of logic applications, but logic is not tuned properly to the new role. In particular, classical logic is preoccupied mostly with infinite static structures whereas many objects of interest in computer science are dynamic objects with bounded resources. This chapter consists of two independent parts. The first part is devoted to finite model theory; it is mostly a survey of logics tailored for computational complexity. The second part is devoted to dynamic structures with bounded resources. In particular, we use dynamic structures with bounded resources to model Pascal.
An Optimal Lower Bound on the Number of Variables for Graph Identification
 Combinatorica
, 1992
"... In this paper we show that Ω(n) variables are needed for firstorder logic with counting to identify graphs on n vertices. The kvariable language with counting is equivalent to the (k − 1)dimensional WeisfeilerLehman method. We thus settle a longstanding open problem. Previously it was an open q ..."
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Cited by 135 (9 self)
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In this paper we show that Ω(n) variables are needed for firstorder logic with counting to identify graphs on n vertices. The kvariable language with counting is equivalent to the (k − 1)dimensional WeisfeilerLehman method. We thus settle a longstanding open problem. Previously it was an open question whether or not 4 variables suffice. Our lower bound remains true over a set of graphs of color class size 4. This contrasts sharply with the fact that 3 variables suffice to identify all graphs of color class size 3, and 2 variables suffice to identify almost all graphs. Our lower bound is optimal up to multiplication by a constant because n variables obviously suffice to identify graphs on n vertices. 1
Linear time solvable optimization problems on graphs of bounded cliquewidth
, 2000
"... Hierarchical decompositions of graphs are interesting for algorithmic purposes. There are several types of hierarchical decompositions. Tree decompositions are the best known ones. On graphs of treewidth at most k, i.e., that have tree decompositions of width at most k, where k is fixed, every dec ..."
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Cited by 112 (22 self)
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Hierarchical decompositions of graphs are interesting for algorithmic purposes. There are several types of hierarchical decompositions. Tree decompositions are the best known ones. On graphs of treewidth at most k, i.e., that have tree decompositions of width at most k, where k is fixed, every decision or optimization problem expressible in monadic secondorder logic has a linear algorithm. We prove that this is also the case for graphs of cliquewidth at most k, where this complexity measure is associated with hierarchical decompositions of another type, and where logical formulas are no longer allowed to use edge set quantifications. We develop applications to several classes of graphs that include cographs and are, like cographs, defined by forbidding subgraphs with “too many” induced paths with four vertices.
Definability with Bounded Number of Bound Variables
 Information and Computation
, 1989
"... A theory satisfies the kvariable property if every firstorder formula is equivalent to a formula with at most k bound variables (possibly reused). Gabbay has shown that a model of temporal logic satisfies the kvariable property for some k if and only if there exists a finite basis for the tempora ..."
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Cited by 77 (6 self)
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A theory satisfies the kvariable property if every firstorder formula is equivalent to a formula with at most k bound variables (possibly reused). Gabbay has shown that a model of temporal logic satisfies the kvariable property for some k if and only if there exists a finite basis for the temporal connectives over that model. We give a modeltheoretic method for establishing the kvariable property, involving a restricted EhrenfeuchtFraisse game in which each player has only k pebbles. We use the method to unify and simplify results in the literature for linear orders. We also establish new kvariable properties for various theories of boundeddegree trees, and in each case obtain tight upper and lower bounds on k. This gives the first finite basis theorems for branchingtime models of temporal logic. 1 Introduction A firstorder theory \Sigma satisfies the kvariable property if every firstorder formula is equivalent under \Sigma to a formula with at most k bound variables (pos...
Toward Logic Tailored for Computational Complexity
 COMPUTATION AND PROOF THEORY
, 1984
"... Whereas firstorder logic was developed to confront the infinite it is often used in computer science in such a way that infinite models are meaningless. We discuss the firstorder theory of finite structures and alternatives to firstorder logic, especially polynomial time logic. ..."
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Cited by 75 (6 self)
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Whereas firstorder logic was developed to confront the infinite it is often used in computer science in such a way that infinite models are meaningless. We discuss the firstorder theory of finite structures and alternatives to firstorder logic, especially polynomial time logic.
The Logic of Games and its Applications
 Annals of Discrete Mathematics
, 1985
"... We develop a Logic in which the basic objects of concern are games, or equivalently, monotone predicate transforms. We give completeness and decision results and extend to certain kinds of manyperson games. Applications to a cake cutting algorithm and to a protocol for exchanging secrets, are given ..."
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Cited by 62 (5 self)
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We develop a Logic in which the basic objects of concern are games, or equivalently, monotone predicate transforms. We give completeness and decision results and extend to certain kinds of manyperson games. Applications to a cake cutting algorithm and to a protocol for exchanging secrets, are given. 1