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52
Integrity Constraints for XML
, 1999
"... this paper, we extend XML DTDs with several classes of integrity constraints and investigate the complexity of reasoning about these constraints. The constraints range over keys, foreign keys, inverse constraints as well as ID constraints for capturing the semantics of object identities. They imp ..."
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Cited by 83 (12 self)
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this paper, we extend XML DTDs with several classes of integrity constraints and investigate the complexity of reasoning about these constraints. The constraints range over keys, foreign keys, inverse constraints as well as ID constraints for capturing the semantics of object identities. They improve semantic specifications and provide a better reference mechanism for native XML applications. They are also useful in information exchange and data integration for preserving the semantics of data originating in relational and objectoriented databases. We establish complexity and axiomatization results for the (finite) implication problems associated with these constraints. In addition, we study implication of more general constraints, such as functional, inclusion and inverse constraints defined in terms of navigation paths
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 76 (5 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...
Path Constraints on Semistructured and Structured Data
, 1998
"... We present a class of path constraints of interest in connection with both structured and semistructured databases, and investigate their associated implication problems. These path constraints are capable of expressing natural integrity constraints that are not only a fundamental part of the semant ..."
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Cited by 63 (18 self)
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We present a class of path constraints of interest in connection with both structured and semistructured databases, and investigate their associated implication problems. These path constraints are capable of expressing natural integrity constraints that are not only a fundamental part of the semantics of the data, but are also important in query optimization. We show that in semistructured databases, despite the simple syntax of the constraints, their associated implication problem is r.e. complete and finite implication problem is cor.e. complete. However, we establish the decidability of the implication problems for several fragments of the path constraint language, and demonstrate that these fragments suffice to express important semantic information such as inverse relationships and local database constraints commonly found in objectoriented databases. We also show that in the presence of types, the analysis of path constraint implication becomes more delicate. We demonst...
Describing Graphs: a FirstOrder Approach to Graph Canonization
, 1990
"... In this paper we ask the question, "What must be added to firstorder logic plus leastfixed point to obtain exactly the polynomialtime properties of unordered graphs?" We consider the languages Lk consisting of firstorder logic restricted to k variables and Ck consisting of Lk plus "counting ..."
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Cited by 57 (7 self)
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In this paper we ask the question, "What must be added to firstorder logic plus leastfixed point to obtain exactly the polynomialtime properties of unordered graphs?" We consider the languages Lk consisting of firstorder logic restricted to k variables and Ck consisting of Lk plus "counting quantifiers". We give efficient canonization algorithms for graphs characterized by Ck or Lk . It follows from known results that all trees and almost all graphs are characterized by C2 .
Infinitary Logic and Inductive Definability over Finite Structures
 Information and Computation
, 1995
"... The extensions of firstorder logic with a least fixed point operator (FO + LFP) and with a partial fixed point operator (FO + PFP) are known to capture the complexity classes P and PSPACE respectively in the presence of an ordering relation over finite structures. Recently, Abiteboul and Vianu [Abi ..."
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Cited by 56 (6 self)
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The extensions of firstorder logic with a least fixed point operator (FO + LFP) and with a partial fixed point operator (FO + PFP) are known to capture the complexity classes P and PSPACE respectively in the presence of an ordering relation over finite structures. Recently, Abiteboul and Vianu [Abiteboul and Vianu, 1991b] investigated the relationship of these two logics in the absence of an ordering, using a machine model of generic computation. In particular, they showed that the two languages have equivalent expressive power if and only if P = PSPACE. These languages can also be seen as fragments of an infinitary logic where each formula has a bounded number of variables, L ! 1! (see, for instance, [Kolaitis and Vardi, 1990]). We investigate this logic of finite structures and provide a normal form for it. We also present a treatment of the results in [Abiteboul and Vianu, 1991b] from this point of view. In particular, we show that we can write a formula of FO + LFP that defines ...
On the Expressive Power of Datalog: Tools and a Case Study
 JOURNAL OF COMPUTER AND SYSTEM SCIENCES
, 1990
"... We study here the language Datalog(6=), which is the query language obtained from Datalog by allowing equalities and inequalities in the bodies of the rules. We view Datalog(6=) as a fragment of an innitary logic L ! and show that L ! can be characterized in terms of certain twoperson pebble ga ..."
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Cited by 52 (9 self)
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We study here the language Datalog(6=), which is the query language obtained from Datalog by allowing equalities and inequalities in the bodies of the rules. We view Datalog(6=) as a fragment of an innitary logic L ! and show that L ! can be characterized in terms of certain twoperson pebble games. This characterization provides us with tools for investigating the expressive power of Datalog(6=). As a case study, we classify the expressibility of fixed subgraph homeomorphism queries on directed graphs. Fortune et al. [FHW80] classied the computational complexity of these queries by establishing two dichotomies, which are proper only if P 6= NP. Without using any complexitytheoretic assumptions, we show here that the two dichotomies are indeed proper in terms of expressibility in Datalog(6=).
Topological Queries in Spatial Databases
 Journal of Computer and System Sciences
, 1996
"... We study topological queries over twodimensional spatial databases. First, we show that the topological properties of semialgebraic spatial regions can be completely specified using a classical finite structure, essentially the embedded planar graph of the region boundaries. This provides an invar ..."
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Cited by 45 (2 self)
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We study topological queries over twodimensional spatial databases. First, we show that the topological properties of semialgebraic spatial regions can be completely specified using a classical finite structure, essentially the embedded planar graph of the region boundaries. This provides an invariant characterizing semialgebraic regions up to homeomorphism. All topological queries on semialgebraic regions can be answered by queries on the invariant whose complexity is polynomially related to the original. Also, we show that for the purpose of answering topological queries, semialgebraic regions can always be represented simply as polygonal regions. We then study query languages for topological properties of twodimensional spatial databases, starting from the topological relationships between pairs of planar regions introduced by Egenhofer. We show that the closure of these relationships under appropriate logical operators yields languages which are complete for topological prope...
Infinitary Logics and 01 Laws
 Information and Computation
, 1992
"... We investigate the in nitary logic L 1! , in which sentences may have arbitrary disjunctions and conjunctions, but they involve only a nite number of distinct variables. We show that various xpoint logics can be viewed as fragments of L 1! , and we describe a gametheoretic characterizat ..."
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Cited by 43 (4 self)
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We investigate the in nitary logic L 1! , in which sentences may have arbitrary disjunctions and conjunctions, but they involve only a nite number of distinct variables. We show that various xpoint logics can be viewed as fragments of L 1! , and we describe a gametheoretic characterization of the expressive power of the logic. Finally, we study asymptotic probabilities of properties 1! on nite structures. We show that the 01 law holds for L 1! , i.e., the asymptotic probability of every sentence in this logic exists and is equal to either 0 or 1. This result subsumes earlier work on asymptotic probabilities for various xpoint logics and reveals the boundary of 01 laws for in nitary logics.