Exact and approximate aggregation in constraint query languages
PODS '99 Proceedings of the eighteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Uniform generation in spatial constraint databases and applications (Extended abstract)
PODS '00 Proceedings of the nineteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Real computations with fake numbers
Journal of Complexity
Uniform generation in spatial constraint databases and applications
Journal of Computer and System Sciences
On the number of random digits required in montecarlo integration of definable functions
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
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The first part of this paper deals with finite-precision arithmetic. We give an upper bound on the precision that should be used in a Monte-Carlo integration method. Such bounds have been known only for convex sets; our bound applies to almost any "reasonable" set. In the second part of the paper, we show how to construct in polynomial time first-order formulas that approximately define the volume of definable sets. This result is based on a VC dimension hypothesis, and is inspired from the well-known complexity-theoretic result "BPP/spl sube//sub 2/". Finally, we show how these results can be applied to sets defined by systems of inequalities involving polynomial or exponential functions. In particular, we describe an application to a problem of structural complexity in the Blum-Shub-Smale model of computation over the reals.