State complexity of the multiples of the Thue-Morse set

03/10/2019

∙

by   Émilie Charlier, et al.

∙

0

∙

share

The Thue-Morse set is the set of those nonnegative integers whose binary expansions have an even number of 1. We obtain an exact formula for the state complexity of the multiplication by a constant of the Thue-Morse set T with respect with any base b which is a power of 2. Our proof is constructive and we are able to explicitly provide the minimal automaton of the language of all 2^p-expansions of the set of integers mT for any positive integers m and p.