RAIRO - Theoretical Informatics and Applications (RAIRO: ITA)

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RAIRO-Theor. Inf. Appl. 42, 481-502 (2008)
DOI: 10.1051/ita:2008015

A new algebraic invariant for weak equivalence of sofic subshifts

Laura Chaubard¹ and Alfredo Costa²

¹ LIAFA, Université Paris VII and CNRS, Case 7014, 2 Place Jussieu, 75251 Paris Cedex 05, France; Laura.Chaubard@liafa.jussieu.fr
² CMUC, Department of Mathematics, University of Coimbra, 3001-454 Coimbra, Portugal; amgc@mat.uc.pt

Published online: 3 June 2008

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 $\zeta$ -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.

Mathematics Subject Classification. 20M07, 37B10, 20M35

Key words: Sofic subshift -- conjugacy -- weak equivalence -- $\zeta$ -semigroup -- pseudovariety.

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