Geodesic
A new algebraic invariant for weak equivalence of sofic subshifts
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 3, pp. 481-502

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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.

DOI : 10.1051/ita:2008015
Classification : 20M07, 37B10, 20M35
Keywords: sofic subshift, conjugacy, weak equivalence, $\zeta $-semigroup, pseudovariety 
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     author = {Chaubard, Laura and Costa, Alfredo},
     title = {A new algebraic invariant for weak equivalence of sofic subshifts},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {481--502},
     publisher = {EDP-Sciences},
     volume = {42},
     number = {3},
     year = {2008},
     doi = {10.1051/ita:2008015},
     mrnumber = {2434031},
     zbl = {1155.37009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ita:2008015/}
}
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Chaubard, Laura; Costa, Alfredo. A new algebraic invariant for weak equivalence of sofic subshifts. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 3, pp. 481-502. doi: 10.1051/ita:2008015

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