Pseudovarieties defining classes of sofic subshifts closed under taking shift equivalent subshifts

摘要

For a pseudovariety V of ordered semigroups, let S(V) be the class of sofic subshifts whose syntactic semigroup lies in V. It is proved that if V contains Sl(-) then S(V * D) is closed under taking shift equivalent subshifts, and conversely, if S(V) is closed under taking conjugate subshifts then V contains LSl(-) and S(V) = S(V * D). Almost finite type subshifts are characterized as the irreducible elements of S(Llnv), which gives a new proof that the class of almost finite type subshifts is closed under taking shift equivalent subshifts. (c) 2006 Elsevier B.V. All rights reserved.