The universal relation is the communication problem in which Alice and Bob get as inputs two distinct strings, and they are required to find a coordinate on which the strings differ. The study of this problem is motivated by its connection to Karchmer-Wigderson relations, which are communication problems that are ... more >>>

In this paper, we propose a new conjecture, the XOR-KRW conjecture, which is a relaxation of the Karchmer-Raz-Wigderson conjecture [KRW95]. This relaxation is still strong enough to imply $\mathbf{P} \not\subseteq \mathbf{NC}^1$ if proven. We also present a weaker version of this conjecture that might be used for breaking $n^3$ lower ... more >>>

One of the major open problems in complexity theory is to demonstrate an explicit function which requires super logarithmic depth, to tackle this problem Karchmer, Raz and Wigderson proposed the KRW conjecture about composition of two functions. While this conjecture seems out of our current reach, some relaxed conjectures are ... more >>>