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Hardness of conjugacy, embedding and factorization of multidimensional subshifts
Abstract : Subshifts of finite type are sets of colorings of the plane defined by local constraints. They can
be
seen as a discretization of continuous dynamical systems. We investigate here the hardness of
deciding factorization, conjugacy and embedding of subshifts in dimensions $d > 1$ for subshifts
of finite type and sofic shifts and in dimensions $d\geq 1$ for effective shifts. In particular, we prove
that the factorization and embedding problems are $\Sigma^0_3$ -complete and $\Sigma^0_1$-
complete respectively for
SFTs, sofic and effective subshifts. Conjugacy on the other side is $\Sigma^0_1$-complete for SFTs and
$\Sigma^0_3$-complete for sofic and effective shifts.
Cited literature [18 references]
https://hal.archives-ouvertes.fr/hal-01150419
Contributor : Pascal Vanier Connect in order to contact the contributor
Submitted on : Friday, June 12, 2015 - 12:46:02 PM
Last modification on : Tuesday, October 19, 2021 - 4:07:14 PM
Long-term archiving on: : Wednesday, April 19, 2017 - 8:32:40 PM
Contributor : Pascal Vanier Connect in order to contact the contributor
Submitted on : Friday, June 12, 2015 - 12:46:02 PM
Last modification on : Tuesday, October 19, 2021 - 4:07:14 PM
Long-term archiving on: : Wednesday, April 19, 2017 - 8:32:40 PM
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