Recent work by Bernasconi, Damm and Shparlinski
proved lower bounds on the circuit complexity of the square-free
numbers, and raised as an open question if similar (or stronger)
lower bounds could be proved for the set of prime numbers. In
this short note, we answer this question ... more >>>

How can we trust the correctness of a learned model on a particular input of interest? Model accuracy is typically measured $on\ average$ over a distribution of inputs, giving no guarantee for any fixed input. This paper proposes a theoretically-founded solution to this problem: to train $Self$-$Proving\ models$ that prove ... more >>>

We show that the GCD of two univariate polynomials can be computed by (piece-wise) algebraic circuits of constant depth and polynomial size over any sufficiently large field, regardless of the characteristic. This extends a recent result of Andrews \& Wigderson who showed such an upper bound over fields of zero ... more >>>