Weizmann Logo
ECCC
Electronic Colloquium on Computational Complexity

Under the auspices of the Computational Complexity Foundation (CCF)

Login | Register | Classic Style



REPORTS > KEYWORD > UNIVERSAL RELATION:
Reports tagged with universal relation:
TR17-128 | 15th August 2017
Or Meir

The Direct Sum of Universal Relations

Revisions: 3 , Comments: 1

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 >>>


TR20-116 | 1st August 2020
Ivan Mihajlin, Alexander Smal

Toward better depth lower bounds: the XOR-KRW conjecture

Revisions: 2

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 >>>


TR23-151 | 11th October 2023
Hao Wu

An Improved Composition Theorem of a Universal Relation and Most Functions via Effective Restriction

Revisions: 1

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 >>>




ISSN 1433-8092 | Imprint