On a continuous Gale--Berlekamp switching game

TL;DR

This paper introduces a continuous variant of the Gale--Berlekamp switching game, explores weighted versions, and provides growth estimates for related optimization problems using deterministic methods, some of which are optimal.

Contribution

It presents a novel continuous version of the classical switching game and analyzes growth estimates for associated optimization problems.

Findings

Growth estimates for the continuous game are established.

Deterministic methods are used to derive these estimates.

Some estimates are proven to be optimal in special cases.

Abstract

We propose a continuous version of the classical Gale--Berlekamp switching game. We also study a weighted version of this new continuous game. The main results of this paper concern growth estimates for the corresponding optimization problems. The methods developed in this article are deterministic in nature and in some special cases the estimates obtained are optimal.