Abstract. By introducing a parallel extension rule that is aware of independence of the introduced extension variables, a calculus for quantified propositional logic is obtained w...
We study the circuit complexity of the powering function, defined as POWm(Z) = Zm for an n-bit integer input Z and an integer exponent m poly(n). Let LTd denote the class of func...
We initiate a direction for proving lower bounds on the size of non-commutative arithmetic circuits. This direction is based on a connection between lower bounds on the size of no...
We study the problem of testing isomorphism (equivalence up to relabelling of the variables) of two Boolean functions f, g : {0, 1}n → {0, 1}. Our main focus is on the most stud...
Any proof of P = NP will have to overcome two barriers: relativization and natural proofs. Yet over the last decade, we have seen circuit lower bounds (for example, that PP does n...