This work presents general techniques for constructing simple to program self-testing/correcting pairs for a variety of numerical functions, including integer multiplication, modular multiplication, matrix multiplication, inverting matrices, computing the determinant of a matrix, Computing the rank of a Matrix, integer division, modular exponentiation, and polynomial multiplication.Expand

This seems simple enough, but let’s play with this definition. The Pythagoreans, an ancient sect of mathematical mystics, said that a number is perfect if it equals the sum of its positive integral… Expand

The characterizations provide results in the area of coding theory by giving extremely fast and efficient error-detecting schemes for some well-known codes and play a crucial role in subsequent results on the hardness of approximating some NP-optimization problems.Expand

A sublinear algorithm which uses O(n/sup 2/3//spl epsiv//sup -4/ log n) independent samples from each distribution, runs in time linear in the sample size, makes no assumptions about the structure of the distributions, and distinguishes the cases when the distance between the distributions is small or large.Expand

The Bloomier filter is introduced, a data structure for compactly encoding a function with static support in order to support approximate evaluation queries and lower bounds are provided to prove the (near) optimality of the constructions.Expand

A new model of learning probability distributions from independent draws is introduced, inspired by the popular Probably Approximately Correct (PAC) model for learning boolean functions from labeled examples, in the sense that it emphasizes efficient and approximate learning, and it studies the learnability of restricted classes of target distributions.Expand

A randomized algorithm is given for solving the task of reconstructing a list of all n-variate degree d polynomials which agree with f on a tiny but non-negligible fraction, /spl delta/, of the input space.Expand

It is shown that in its most general setting, testing that Boolean functions are close to monotone is equivalent, with respect to the number of required queries, to several other testing problems in logic and graph theory.Expand

This work presents spot-checkers for sorting, convex hull, element distinctness, set containment, set equality, total orders, and correctness of group and field operations and shows that the spot-checking model can be applied to problems in a wide range of areas, including problems regarding graphs, sets, and algebra.Expand