D a t a b a s e Theory Column* Query Languages with Arithmetic and Constraint Databases Leonid Libkin Bell Laboratories 600 Mountain Avenue Murray Hill, NJ 07974 E-maih libkin~resea~ch.bell-labs.com Introduction Can we store an infinite set in a database? Clearly not, b u t instead we can store a finite representation of an infinite set and write queries as if t h e entire infinite set were stored. This is the key idea b e h i n d constraint databases, which e m e r g e d relatively recently as a very active area of d a t a b a s e research. T h e p r i m a r y m o t i v a t i o n comes f~om geographical and t e m p o r a l databases: how does one store a region in a database? More importantly, how does one design a query language t h a t makes the user view a region as it if were an infinite collection of points stored in the database? Finite representations used in constraint databases are first-order formulae; in geographical applications, one often uses Boolean combinations
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