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A new algebraic invariant for weak equivalence of sofic subshifts

Published online by Cambridge University Press:  03 June 2008

Laura Chaubard
Affiliation:
LIAFA, Université Paris VII and CNRS, Case 7014, 2 Place Jussieu, 75251 Paris Cedex 05, France; Laura.Chaubard@liafa.jussieu.fr
Alfredo Costa
Affiliation:
CMUC, Department of Mathematics, University of Coimbra, 3001-454 Coimbra, Portugal; amgc@mat.uc.pt
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Abstract

It is studied how taking the inverse image by a sliding block code affects the syntactic semigroup of a sofic subshift. The main tool are ζ-semigroups, considered as recognition structures for sofic subshifts. 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.

Type
Research Article
Copyright
© EDP Sciences, 2008

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