Resumen de Coordination through De Bruijn Sequences

Olivier Gossner, Penélope Hernández Rojas

• Let µ be a rational distribution over a finite alphabet, and ( ) be a n-periodic sequences which first n elements are drawn i.i.d. according to µ. We consider automata of bounded size that input and output at stage t. We prove the existence of a constant C such that, whenever , with probability close to 1 there exists an automaton of size m such that the empirical frequency of stages such that is close to 1. In particular, one can take , where and .