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Article Dans Une Revue Journal of Computer and System Sciences Année : 2015

Hardness of conjugacy, embedding and factorization of multidimensional subshifts

Résumé

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.
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Dates et versions

hal-01150419 , version 1 (12-06-2015)

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Emmanuel Jeandel, Pascal Vanier. Hardness of conjugacy, embedding and factorization of multidimensional subshifts . Journal of Computer and System Sciences, 2015, http://dx.doi.org/10.1016/j.jcss.2015.05.003. ⟨10.1016/j.jcss.2015.05.003⟩. ⟨hal-01150419⟩
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