The reliability of database queries on databases with uncertain information is studied, on the basis of a probabilistic model for unreliable databases. While it was already known that the reliability of quantifierfree queries is computable in polynomial time, we show here that already for conjunctive queries, the reliability may become highly intractable. We exhibit a conjunctive query whose reliability problem is complete for FP #P . We further show, that FP #P is the typical complexity level for the reliability problems of a very large class of queries, including all second-order queries. We study approximation algorithms and prove that the reliabilities of all polynomial-time evaluable queries can be efficiently approximated by randomized algorithms. Finally we discuss the extension of our approach to the more general metafinite database model where finite relational structures are endowed with functions into an infinite interpreted domain; in addition queries may use aggregate ...

Gap-definability and the gap-closure operator were defined in [FFK94]. Few complexity classes were known at that time to be gap-definable. In this paper, we give simple characterizations of both gapdefinability and the gap-closure operator, and we show that many complexity classes are gap-definable, including P #P , P #P[1] , PSPACE, EXP, NEXP, MP (Middle-bit P), and BP\Delta\PhiP. If a class is closed under union, intersection and contains ; and \Sigma , then it is gap-definable if and only if it contains SPP; its gap-closure is the closure of this class together with SPP under union and intersection. On the other hand, we give some examples of classes which are reasonable gap-definable but not closed under union (resp. intersection, complement). Finally, we show that a complexity class such as PSPACE or PP, if it is not equal to SPP, contains a maximal gap-definable many-one reduction-closed subclass, which is properly between SPP and the class of all PSPACE-incomplete (PP-in...

The reliability of database queries on databases with uncertain information is studied, on the basis of a probabilistic model for unreliable databases.

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