Synchronizing delay for binary uniform morphisms

Klouda, Karel; Medková, Kateřina

doi:10.1016/j.tcs.2015.11.043

“…with j q −r q , i q −r q belonging to E(x, σ). By applying σ to these two word, we thus obtain (10), which ends the proof.…”

Section: Proof Of Theoremmentioning

confidence: 64%

“…We now show that [j q − r q , j q + s q ] ∩ E(x, σ) = ([i q − r q , i q + s q ] ∩ E(x, σ)) − (i q − j q ). (10) This will contradict the fact that i q belongs to E(x, σ) and j q does not. By ( 6), we have…”

Section: Proof Of Theoremmentioning

confidence: 95%

The constant of recognizability is computable for primitive morphisms

Durand,

Leroy

2016

Preprint

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“…In [KM16] better bounds are given for the case of constant length substitutions on a two letter alphabet but in terms of "synchronization delay" and "circularity". As the recognizability constant is bounded by the synchronization delay (see comments in [DL17]), this gives the following theorem that greatly improves our bounds.…”

Section: Theorem 46 ([Dl17]mentioning

confidence: 99%

Untitled

2022

discrete_Anal

0

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Classification is a central problem for dynamical systems, in particular for families that arise in a wide range of topics, like substitution subshifts. It is important to be able to distinguish whether two such subshifts are isomorphic, but the existing invariants are not sufficient for this purpose. We first show that given two minimal substitution subshifts, there exists a computable constant R such that any factor map between these subshifts (if any) is the composition of a factor map with a radius smaller than R and some power of the shift map. Then we prove that it is decidable to check whether a given sliding block code is a factor map between two prescribed minimal substitution subshifts. As a consequence of these two results, we provide an algorithm that, given two minimal substitution subshifts, decides whether one is a factor of the other and, as a straightforward corollary, whether they are isomorphic.

show abstract

“…In [KM16] better bounds are given for the two letter alphabet but in terms of "synchronization delay" and "circularity". As the recognizability constant is bounded by the synchronization delay (see comments in [DL17]), this gives the following theorem that greatly improves our bounds.…”

Section: [Mos92]mentioning

confidence: 99%

Decidability of the isomorphism and the factorization between minimal substitution subshifts

Durand¹,

Leroy²

2018

Preprint

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Classification is a central problem for dynamical systems, in particular for families that arise in a wide range of topics, like substitution subshifts. It is important to be able to distinguish whether two such subshifts are isomorphic, but the existing invariants are not sufficient for this purpose. We first show that given two minimal substitution subshifts, there exists a computable constant R such that any factor map between these subshifts (if any) is the composition of a factor map with a radius smaller than R and some power of the shift map. Then we prove that it is decidable to check whether a given sliding block code is a factor map between two prescribed minimal substitution subshifts. As a consequence of these two results, we provide an algorithm that, given two minimal substitution subshifts, decides whether one is a factor of the other and, as a straightforward corollary, whether they are isomorphic.

show abstract

Synchronizing delay for binary uniform morphisms

Cited by 4 publications

References 12 publications

The constant of recognizability is computable for primitive morphisms

The constant of recognizability is computable for primitive morphisms

Untitled

Decidability of the isomorphism and the factorization between minimal substitution subshifts

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