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105
ConjunctiveQuery Containment and Constraint Satisfaction
 Journal of Computer and System Sciences
, 1998
"... Conjunctivequery containment is recognized as a fundamental problem in database query evaluation and optimization. At the same time, constraint satisfaction is recognized as a fundamental problem in artificial intelligence. What do conjunctivequery containment and constraint satisfaction have in c ..."
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Cited by 131 (13 self)
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Conjunctivequery containment is recognized as a fundamental problem in database query evaluation and optimization. At the same time, constraint satisfaction is recognized as a fundamental problem in artificial intelligence. What do conjunctivequery containment and constraint satisfaction have in common? Our main conceptual contribution in this paper is to point out that, despite their very different formulation, conjunctivequery containment and constraint satisfaction are essentially the same problem. The reason is that they can be recast as the following fundamental algebraic problem: given two finite relational structures A and B, is there a homomorphism h : A ! B? As formulated above, the homomorphism problem is uniform in the sense that both relational structures A and B are part of the input. By fixing the structure B, one obtains the following nonuniform problem: given a finite relational structure A, is there a homomorphism h : A ! B? In general, nonuniform tractability results do not uniformize. Thus, it is natural to ask: which tractable cases of nonuniform tractability results for constraint satisfaction and conjunctivequery containment do uniformize? Our main technical contribution in this paper is to show that several cases of tractable nonuniform constraint satisfaction problems do indeed uniformize. We exhibit three nonuniform tractability results that uniformize and, thus, give rise to polynomialtime solvable cases of constraint satisfaction and conjunctivequery containment.
Relational Expressive Power of Constraint Query Languages
 Journal of the ACM
, 1995
"... The expressive power of firstorder query languages with several classes of equality and inequality constraints is studied in this paper. We settle the conjecture that recursive queries such as parity test and transitive closure cannot be expressed in the relational calculus augmented with polynomia ..."
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Cited by 77 (18 self)
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The expressive power of firstorder query languages with several classes of equality and inequality constraints is studied in this paper. We settle the conjecture that recursive queries such as parity test and transitive closure cannot be expressed in the relational calculus augmented with polynomial inequality constraints over the reals. Furthermore, noting that relational queries exhibit several forms of genericity, we establish a number of collapse results of the following form: The class of generic boolean queries expressible in the relational calculus augmented with a given class of constraints coincides with the class of queries expressible in the relational calculus (with or without an order relation). We prove such results for both the natural and activedomain semantics. As a consequence, the relational calculus augmented with polynomial inequalities expresses the same classes of generic boolean queries under both the natural and activedomain semantics. In the course of proving...
Deciding FirstOrder Properties of Locally TreeDecomposable Graphs
 In Proc. 26th ICALP
, 1999
"... . We introduce the concept of a class of graphs being locally treedecomposable. There are numerous examples of locally treedecomposable classes, among them the class of planar graphs and all classes of bounded valence or of bounded treewidth. We show that for each locally treedecomposable cl ..."
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Cited by 75 (12 self)
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. We introduce the concept of a class of graphs being locally treedecomposable. There are numerous examples of locally treedecomposable classes, among them the class of planar graphs and all classes of bounded valence or of bounded treewidth. We show that for each locally treedecomposable class C of graphs and for each property ' of graphs that is denable in rstorder logic, there is a linear time algorithm deciding whether a given graph G 2 C has property '. 1 Introduction It is an important task in the theory of algorithms to nd feasible instances of otherwise intractable algorithmic problems. A notion that has turned out to be extremely useful in this context is that of treewidth of a graph. 3Colorability, Hamiltonicity, and many other NPcomplete properties of graphs can be decided in linear time when restricted to graphs whose treewidth is bounded by a xed constant (see [Bod97] for a survey). Courcelle [Cou90] proved a metatheorem, which easily implies numer...
On the Expressive Completeness of the Propositional MuCalculus With Respect to Monadic Second Order Logic
, 1996
"... . Monadic second order logic (MSOL) over transition systems is considered. It is shown that every formula of MSOL which does not distinguish between bisimilar models is equivalent to a formula of the propositional calculus. This expressive completeness result implies that every logic over tran ..."
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Cited by 65 (3 self)
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. Monadic second order logic (MSOL) over transition systems is considered. It is shown that every formula of MSOL which does not distinguish between bisimilar models is equivalent to a formula of the propositional calculus. This expressive completeness result implies that every logic over transition systems invariant under bisimulation and translatable into MSOL can be also translated into the calculus. This gives a precise meaning to the statement that most propositional logics of programs can be translated into the calculus. 1 Introduction Transition systems are structures consisting of a nonempty set of states, a set of unary relations describing properties of states and a set of binary relations describing transitions between states. It was advocated by many authors [26, 3] that this kind of structures provide a good framework for describing behaviour of programs (or program schemes), or even more generally, engineering systems, provided their evolution in time is disc...
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=).
L.: Locally consistent transformations and query answering in data exchange
 In: Proceedings PODS’04
, 2004
"... Data exchange is the problem of taking data structured under a source schema and creating an instance of a target schema. Given a source instance, there may be many solutions – target instances that satisfy the constraints of the data exchange problem. Previous work has identified two classes of des ..."
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Cited by 48 (17 self)
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Data exchange is the problem of taking data structured under a source schema and creating an instance of a target schema. Given a source instance, there may be many solutions – target instances that satisfy the constraints of the data exchange problem. Previous work has identified two classes of desirable solutions: canonical universal solutions, and their cores. Query answering in data exchange amounts to rewriting a query over the target schema to another query that, over a materialized target instance, gives the result that is semantically consistent with the source. A basic question is then whether there exists a transformation sending a source instance into a solution over which target queries can be answered. We show that the answer is negative for many data exchange transformations that have structural properties similar to canonical universal solutions and cores. Namely, we prove that many such transformations preserve the local structure of the data. Using this notion, we further show that every target query rewritable over such a transformation cannot distinguish tuples whose neighborhoods in the source are similar. This gives us a first tool that helps check whether a query is rewritable. We also show that these results are robust: they hold for an extension of relational calculus with grouping and aggregates, and for two different semantics of query answering. 1.
New Techniques for Studying Set Languages, Bag Languages and Aggregate Functions
, 1994
"... We provide new techniques for the analysis of the expressive power of query languages for nested collections. These languages may use set or bag semantics and may be further complicated by the presence of aggregate functions. We exhibit certain classes of graphs and prove that the properties of thes ..."
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Cited by 42 (25 self)
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We provide new techniques for the analysis of the expressive power of query languages for nested collections. These languages may use set or bag semantics and may be further complicated by the presence of aggregate functions. We exhibit certain classes of graphs and prove that the properties of these graphs that can be tested in such languages are either finite or cofinite. This result settles the conjectures of Grumbach, Milo, and Paredaens that parity test, transitive closure, and balanced binary tree test are not expressible in bag languages like the PTIME fragment of BALG of Grumbach and Milo and BQL of Libkin and Wong. Moreover, it implies that many recursive queries, including simple ones like the test for a chain, cannot be expressed in a nested relational language even when aggregate functions are available. In an attempt to generalize the finitecofiniteness result, we study the bounded degree property which says that the number of distinct in and outdegrees in the output of...
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 42 (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.
Local Properties of Query Languages
"... predeterminedportionoftheinput.Examplesincludeallrelationalcalculusqueries. everyrelationalcalculus(rstorder)queryislocal,thegeneralresultsprovedforlocalqueriescan manyeasyinexpressibilityproofsforlocalqueries.Wethenconsideracloselyrelatedproperty, namely,theboundeddegreeproperty.Itdescribestheoutp ..."
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Cited by 33 (21 self)
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predeterminedportionoftheinput.Examplesincludeallrelationalcalculusqueries. everyrelationalcalculus(rstorder)queryislocal,thegeneralresultsprovedforlocalqueriescan manyeasyinexpressibilityproofsforlocalqueries.Wethenconsideracloselyrelatedproperty, namely,theboundeddegreeproperty.Itdescribestheoutputsoflocalqueriesonstructuresthat locallylook\simple."Everyquerythatislocalisshowntohavetheboundeddegreeproperty.Since Westartbyprovingageneralresultdescribingoutputsoflocalqueries.Thisresultleadsto toapplythanEhrenfeuchtFrassegames.Wealsoshowthatsomegeneralizationsofthebounded degreepropertythatwereconjecturedtohold,failforrelationalcalculus. beviewedas\otheshelf"strategiesforprovinginexpressibilityresults,whichareofteneasier maintenanceofviews,andshowthatSQLandrelationalcalculusareincapableofmaintainingthe gregates,whichisessentiallyplainSQL,hastheboundeddegreeproperty,thusansweringaques tionthathasbeenopenforseveralyears.Consequently,rstorderquerieswithHartigorRescher quantiersalsohavetheboundeddegreeproperty.Finally,weapplyourresultstoincremental Wethenprovethatthelanguageobtainedfromrelationalcalculusbyaddinggroupingandag