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On the Implementation of Huge Random Objects

Author(s)
Goldreich, Oded; Goldwasser, Shafi; Nussboim, Asaf
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Abstract
We initiate a general study of the feasibility of implementing (huge) random objects, and demonstrate its applicability to a number of areas in which random objects occur naturally. We highlight two types of measures of the quality of the implementation (with respect to the desired specification): The first type corresponds to various standard notions of indistinguishability (applied to function ensembles), whereas the second type is a novel notion that we call truthfulness. Intuitively, a truthful implementation of a random object of Type T must (always) be an object of Type T, and not merely be indistinguishable from a random object of Type T. Our formalism allows for the consideration of random objects that satisfy some fixed property (or have some fixed structure) as well as the consideration of objects supporting complex queries. For example, we consider the truthful implementation of random Hamiltonian graphs as well as supporting complex queries regarding such graphs (e.g., providing the next vertex along a fixed Hamiltonian path in such a graph).
Date issued
2010-05
URI
http://hdl.handle.net/1721.1/60920
Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Journal
SIAM Journal on Computing
Publisher
Society of Industrial and Applied Mathematics (SIAM)
Citation
Goldreich, Oded, Shafi Goldwasser, and Asaf Nussboim. “On the Implementation of Huge Random Objects.” SIAM Journal on Computing 39.7 (2010): 2761-2822. © 2010 Society for Industrial and Applied Mathematics
Version: Final published version
ISSN
0097-5397
1095-7111

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