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Author(s)
Alfredo Costa; Laura Chaubard;
Title A new algebraic invariant for weak equivalence of sofic subshifts
Abstract It is studied how taking the inverse image by a sliding block code affects the syntactic semigroup of a sofic subshift. Two independent approaches are used: zsemigroups as recognition structures for sofic subshifts, and relatively free profinite semigroups. A new algebraic invariant is obtained for weak equivalence of sofic subshifts, by determining which classes of sofic subshifts naturally defined by pseudovarieties of finite semigroups are closed under weak equivalence. Among such classes are the classes of almost finite type subshifts and aperiodic subshifts.
The algebraic invariant is compared with other robust conjugacy invariants.
Preprint series Prépublicações do Departamento de Matemática da Universidade de Coimbra
Issue 0657
Year 2006
