This paper describes recent results which revolve around the question of the rate attainable by families of error correcting codes that are locally testable. Emphasis is placed on motivating the problem of proving upper bounds on the rate of these codes and a number of interesting open questions for future ... more >>>

This paper is our second step towards developing a theory of
testing monomials in multivariate polynomials. The central
question is to ask whether a polynomial represented by an
arithmetic circuit has some types of monomials in its sum-product
expansion. The complexity aspects of this problem and its variants
have been ... more >>>

We describe a reduction from the problem of unordered search(with a unique solution) to the problem of inverting a permutation. Since there is a straightforward reduction in the reverse direction, the problems are essentially equivalent.

The reduction helps us bypass the Bennett-Bernstein-Brassard-Vazirani hybrid argument (1997} and the Ambainis quantum adversary ... more >>>