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SelfTesting/Correcting with Applications to Numerical Problems
, 1990
"... Suppose someone gives us an extremely fast program P that we can call as a black box to compute a function f . Should we trust that P works correctly? A selftesting/correcting pair allows us to: (1) estimate the probability that P (x) 6= f(x) when x is randomly chosen; (2) on any input x, compute ..."
Abstract

Cited by 340 (26 self)
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Suppose someone gives us an extremely fast program P that we can call as a black box to compute a function f . Should we trust that P works correctly? A selftesting/correcting pair allows us to: (1) estimate the probability that P (x) 6= f(x) when x is randomly chosen; (2) on any input x, compute f(x) correctly as long as P is not too faulty on average. Furthermore, both (1) and (2) take time only slightly more than Computer Science Division, U.C. Berkeley, Berkeley, California 94720, Supported by NSF Grant No. CCR 8813632. y International Computer Science Institute, Berkeley, California 94704 z Computer Science Division, U.C. Berkeley, Berkeley, California 94720, Supported by an IBM Graduate Fellowship and NSF Grant No. CCR 8813632. the original running time of P . We present general techniques for constructing simple to program selftesting /correcting pairs for a variety of numerical problems, including integer multiplication, modular multiplication, matrix multiplicatio...
Program Result Checking Against Adaptive Programs and in Cryptographic Settings (Extended Abstract)
 In DIMACS Workshop on Distributed Computing and Crypthography
, 1990
"... ) Manuel Blum Computer Science Division U.C. Berkeley Berkeley, California 94720 Michael Luby International Computer Science Institute Berkeley, California 94704 Ronitt Rubinfeld y Computer Science Division U.C. Berkeley Berkeley, California 94720 May 17, 1990 Abstract The theory of p ..."
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Cited by 14 (4 self)
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) Manuel Blum Computer Science Division U.C. Berkeley Berkeley, California 94720 Michael Luby International Computer Science Institute Berkeley, California 94704 Ronitt Rubinfeld y Computer Science Division U.C. Berkeley Berkeley, California 94720 May 17, 1990 Abstract The theory of program result checking introduced in [Blum] allows one to check that a program P correctly computes the function f on input x. The checker may use P 's outputs on other inputs to help it check that P (x) = f(x). In this setting, P is always assumed to be a fixed program, whose output on input x is a function P (x). We extend the theory to check a program P which returns a result on input x that may depend on previous questions asked of P . We call a checker that works for such a program an adaptive checker. We consider the case where there is an adaptive program that supposedly computes f running on each of several noninteracting machines. We design adaptive checkers that work for a c...