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 >>>

In this work, we study the problem of testing $m$-\emph{grainedness} of probability distributions over an $n$-element universe $\mathcal{U}$, or, equivalently, of whether a probability distribution is induced by a multiset $S\subseteq \mathcal{U}$ of size $|S|=m$. Recently, Goldreich and Ron (Computational Complexity, 2023) proved that $\Omega(n^c)$ samples are necessary for testing ... more >>>