Infinite Communication Complexity
Computational Complexity
2015-01-26 v1 Discrete Mathematics
Abstract
Suppose that Alice and Bob are given each an infinite string, and they want to decide whether their two strings are in a given relation. How much communication do they need? How can communication be even defined and measured for infinite strings? In this article, we propose a formalism for a notion of infinite communication complexity, prove that it satisfies some natural properties and coincides, for relevant applications, with the classical notion of amortized communication complexity. More-over, an application is given for tackling some conjecture about tilings and multidimensional sofic shifts.
Cite
@article{arxiv.1501.05814,
title = {Infinite Communication Complexity},
author = {Pierre Guillon and Emmanuel Jeandel},
journal= {arXiv preprint arXiv:1501.05814},
year = {2015}
}
Comments
First Version. Written from the Computer Science POV