A coloring of a graph is {\it convex} if it induces a partition of the vertices into connected subgraphs. Besides being an interesting property from a theoretical point of view, tests for convexity have applications in various areas involving large graphs. Our results concern the important subcase of testing for ... more >>>

A property tester with high probability accepts inputs satisfying a given property and rejects inputs that are far from satisfying it. A tolerant property tester, as defined by Parnas, Ron and Rubinfeld, must also accept inputs that are close enough to satisfying the property. We construct properties of binary functions ... more >>>

Using a new statistical embedding of words which has similarities with the Parikh mapping, we first construct a tolerant tester for the equality of two words, whose complexity is independent of the string size, where the distance between inputs is measured by the normalized edit distance with moves. As a ... more >>>

An $\epsilon$-test for a property $P$ of functions from ${\cal D}=\{1,\ldots,d\}$ to the positive integers is a randomized algorithm, which makes queries on the value of an input function at specified locations, and distinguishes with high probability between the case of the function satisfying $P$, and the case that it ... more >>>

Let $P$ be a property of graphs. An $\epsilon$-test for $P$ is a randomized algorithm which, given the ability to make queries whether a desired pair of vertices of an input graph $G$ with $n$ vertices are adjacent or not, distinguishes, with high probability, between the case of $G$ satisfying ... more >>>

This paper strengthens the low-error PCP characterization of NP, coming closer to the ultimate BGLR conjecture. Namely, we prove that witnesses for membership in any NP language can be verified with a constant number of accesses, and with an error probability exponentially small in the number of bits accessed, as ... more >>>