In this note, we use lower bounds on Boolean multiplicative complexity to prove lower bounds on Boolean circuit complexity. We give a very simple proof of a 7n/3 − c lower bound ...
Consider the following two-player communication process to decide a language L: The first player holds the entire input x but is polynomially bounded; the second player is computa...
—In 1982, Kannan showed that ΣP 2 does not have nk -sized circuits for any k. Do smaller classes also admit such circuit lower bounds? Despite several improvements of Kannan’s...
Every symplectic spread of PG(3, q), or equivalently every ovoid of Q(4, q), is shown to give a certain family of permutation polynomials of GF(q) and conversely. This leads to an...
In this paper, we offer an exposition of a theorem originally due to Adleman, Demarrais and Huang that shows that the quantum complexity class BQP (Bounded-error Quantum Polynomia...