We study query-to-communication lifting. The major open problem in this area is to prove a lifting theorem for gadgets of constant size. The recent paper (Beame, Koroth, 2023) introduces semi-structured communication complexity, in which one of the players can only send parities of their input bits. They have shown that ... more >>>

In this paper, we address the black-box polynomial identity testing (PIT) problem for non-commutative polynomials computed by $+$-regular circuits, a class of homogeneous circuits introduced by Arvind, Joglekar, Mukhopadhyay, and Raja (STOC 2017, Theory of Computing 2019). These circuits can compute polynomials with a number of monomials that are doubly ... more >>>

For a polynomial $f$ from a class $\mathcal{C}$ of polynomials, we show that the problem to compute all the constant degree irreducible factors of $f$ reduces in polynomial time to polynomial identity tests (PIT) for class $\mathcal{C}$ and divisibility tests of $f$ by constant degree polynomials. We apply the result ... more >>>