Infinite Communication Complexity

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.Comment: First Version. Written from the Computer Science PO

Subshifts with sparse traces

We study two-dimensional subshifts whose horizontal trace (also called projective subdynamics) contains only configurations of finite support. Our main result is a classification result for such subshifts satisfying a minimality property. As corollaries, we obtain new proofs for various known results on traces of SFTs, nilpotency, and decidability results for cellular automata and topological full groups. We also construct various (sofic) examples illustrating the concepts