A new algebraic invariant for weak equivalence of sofic subshifts

Laura Chaubard; Alfredo Costa

RAIRO - Theoretical Informatics and Applications (2008)

  • Volume: 42, Issue: 3, page 481-502
  • ISSN: 0988-3754

Abstract

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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.

How to cite

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Chaubard, Laura, and Costa, Alfredo. "A new algebraic invariant for weak equivalence of sofic subshifts." RAIRO - Theoretical Informatics and Applications 42.3 (2008): 481-502. <http://eudml.org/doc/250340>.

@article{Chaubard2008,
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. },
author = {Chaubard, Laura, Costa, Alfredo},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Sofic subshift; conjugacy; weak equivalence; ζ-semigroup; pseudovariety.; sofic subshift; -semigroup; pseudovarieties of finite semigroups},
language = {eng},
month = {6},
number = {3},
pages = {481-502},
publisher = {EDP Sciences},
title = {A new algebraic invariant for weak equivalence of sofic subshifts},
url = {http://eudml.org/doc/250340},
volume = {42},
year = {2008},
}

TY - JOUR
AU - Chaubard, Laura
AU - Costa, Alfredo
TI - A new algebraic invariant for weak equivalence of sofic subshifts
JO - RAIRO - Theoretical Informatics and Applications
DA - 2008/6//
PB - EDP Sciences
VL - 42
IS - 3
SP - 481
EP - 502
AB - 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.
LA - eng
KW - Sofic subshift; conjugacy; weak equivalence; ζ-semigroup; pseudovariety.; sofic subshift; -semigroup; pseudovarieties of finite semigroups
UR - http://eudml.org/doc/250340
ER -

References

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