By Gabriel Kuper, Leonid Libkin, Jan Paredaens

ISBN-10: 3642085423

ISBN-13: 9783642085420

ISBN-10: 366204031X

ISBN-13: 9783662040317

This booklet is the 1st complete survey of the sphere of constraint databases. Constraint databases are a pretty new and energetic zone of database learn. the major proposal is that constraints, resembling linear or polynomial equations, are used to symbolize huge, or maybe endless, units in a compact approach. the power to accommodate limitless units makes constraint databases rather promising as a know-how for integrating spatial and temporal info with usual re lational databases. Constraint databases deliver thoughts from various fields, resembling common sense and version thought, algebraic and computational geometry, in addition to symbolic computation, to the layout and research of knowledge versions and question languages. The ebook is a collaborative attempt concerning many authors who've con tributed chapters on their fields of craftsmanship. regardless of this, the ebook is designed to be learn as a complete, rather than a suite of person surveys. In par ticular, the terminology and the fashion of presentation were standardized, and there are a number of cross-references among the chapters. the assumption of constraint databases is going again to the past due Paris Kanellakis.

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**Example text**

I=l - If n encodes an atomic formula of the form t 1 = t 2 , then perform Formula:= Formula U {(n,x,y) 1\ I Counter(n) 2 2 i=l i=l 1\ Counteri(ni) 1\ 3z(l\ Term(ni, x, y, z)))} . 3n13n2( - If n encodes an atomic formula of the form p( h, ... , tr), then perform Formula:= Formula U {(n,x,y) r I Counter(n) 1\ 3nl .. 3nr(l\ Counteri(ni) i=l r 1\ 3zl ... 3zr( 1\ Term(ni, x, y, Zi) 1\ p(z1, ... , Zr )))} . i=l - If n encodes a formula of the form 'lj; 1 V 'lj; 2 , then, supposing the encodings of subformulae 'lj; 1 and 'lj; 2 are stored in counter variables Counter 1 and Counter 2 respectively, perform Formula:= Formula U {(n,x,y) I Counter(n) 2 1\ 3n13n2(/\ Counteri(ni) 1\ i=l 2 (V Formula(ni,x,y)))}.

8 Historical Note The research into constraint databases started with the goal of defining a database version of CLP, along the same lines as the definition of DATALOG as a database version of Prolog. The original goal was to use bottom-up techniques for processing DATALOG rules in a constraint setting, thus making it possible to use CLP programs in applications where data could be represented as large sets of constraints (for example, spatial data) . As the research progressed it turned out that the problem of handling recursion in 16 Kuper, Libkin, and Paredaens the presence of constraints did not lend itself to a good solution, and as a result the field developed in a different direction, focusing primarily on the nonrecursive case.

If the relational calculus over M can express finiteness, then constraint-satisfiability (and equivalence) of relational calculus formulae over M is undecidable for any schema containing at least one relation name of arity 2: 2. Proof. Let

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