## Self-Testing/Correcting with Applications to Numerical Problems (1990)

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Citations: | 345 - 27 self |

### BibTeX

@MISC{Blum90self-testing/correctingwith,

author = {Manuel Blum and Michael Luby and Ronitt Rubinfeld},

title = {Self-Testing/Correcting with Applications to Numerical Problems},

year = {1990}

}

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### Abstract

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 self-testing/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 88-13632. 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 88-13632. 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...