Linear vs . Order Constraint Queries Over
نویسندگان
چکیده
We consider relational databases organized over an ordered domain with some additional relations|a typical example is the ordered domain of rational numbers together with the ternary relation + of addition. In the focus of our study are the rst order queries that are invariant under order-preserving \permutations"|such queries are called (order-)generic. We show that for an arbitrary ordered divisible Abelian group order-generic queries fail to express more than pure order queries, and that, moreover, the generic queries can be eeectively translated into pure order queries. For example, every order-generic query over rational numbers with + can be eeectively rewritten without +. An important diierence of this paper from a recent series of related papers (see, for example, PVV95, BDLW96]) is that we generalize all notions to the case of nitely representable database states|as opposed to nite states| and develop a general lifting technique that, essentially, allows us to extend any result of the kind we are interested in, from nite to nitely-representable states, and thus all the results in this paper are proved for the general case of constraint databases. This lifting technique relies upon a geometrically clear representation of nitely representable (but possibly innnite) relations over an arbitrary ordered domain in the form of nite relations. The translation of one representation into another is shown to be uniform rst order. The value of these results is not limited to the speciic set of problems considered in this paper, as a matter of fact, they show that order-constraint and nite databases are equally powerful| although the constraint representation does provide a more intuitive user interface.
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