Polynomial factorization is a fundamental problem in computational algebra. Over the past half century, a variety of algorithmic techniques have been developed to tackle different variants of this problem. In parallel, algebraic complexity theory classifies polynomials into complexity classes based on their perceived `hardness'. This raises a natural question: Do ... more >>>

A Boolean predicate $A$ is defined to be promise-useful if $PCSP(A,B)$ is tractable for some non-trivial $B$ and otherwise it is promise-useless. We initiate investigations of this notion and derive sufficient conditions for both promise-usefulness and promise-uselessness (assuming $\text{P} \ne \text{NP}$). While we do not obtain a complete characterization, our ... more >>>

Quantum versus classical separation plays a central role in understanding the advantages of quantum computation. In this paper, we present the first exponential separation between quantum and bounded-error randomized communication complexity in a variant of the Number-on-Forehead (NOF) model. Namely, the three-player Simultaneous Number-on-Forehead model. Specifically, we introduce the Gadgeted ... more >>>