Conjugacy invariants of subshifts: an approach from profinite semigroup theory

Abstract

It is given a structural conjugacy invariant in the set of pseudowords whose nite factors are factors of a given subshift. Some pro nite semigroup tools are developed for this purpose. With these tools a shift equivalence invariant of so c subshifts is obtained, improving an invariant introduced by B eal, Fiorenzi and Perrin using di erent techniques. This new invariant is used to prove that some irreducible almost nite type subshifts with the same entropy and the same zeta function are not shift equivalent.