We study testing of local properties in one-dimensional and multi-dimensional arrays. A property of $d$-dimensional arrays $f:[n]^d \to \Sigma$ is $k$-local if it can be defined by a family of $k \times \ldots \times k$ forbidden consecutive patterns. This definition captures numerous interesting properties. For example, monotonicity, Lipschitz continuity and ... more >>>

We initiate the study of the role of erasures in local decoding and use our understanding to prove a separation between erasure-resilient and tolerant property testing. Local decoding in the presence of errors has been extensively studied, but has not been considered explicitly in the presence of erasures.

Motivated by ... more >>>

We prove anti-concentration for the inner product of two independent random vectors in the discrete cube. Our results imply Chakrabarti and Regev's lower bound on the randomized communication complexity of the gap-hamming problem. They are also meaningful in the context of randomness extraction. The proof provides a framework for establishing ... more >>>