We show that there is a randomized algorithm that, when given a small constant-depth Boolean circuit $C$ made up of gates that compute constant-degree Polynomial Threshold functions or PTFs (i.e., Boolean functions that compute signs of constant-degree polynomials), counts the number of satisfying assignments to $C$ in significantly better than ... more >>>

The problem of verifiable delegation of computation considers a setting in which a client wishes to outsource an expensive computation to a powerful, but untrusted, server. Since the client does not trust the server, we would like the server to certify the correctness of the result. Delegation has emerged as ... more >>>

We define new functions based on the Andreev function and prove that they require $n^{3}/polylog(n)$ formula size to compute. The functions we consider are generalizations of the Andreev function using compositions with the majority function. Our arguments apply to composing a hard function with any function that agrees with the ... more >>>