Intertwined Synchronized Systems
Dastjerdi, D. Ahmadi · Shaldehi, S. Jangjooye
Original · EN
An asymmetric-RLL(d₁,k₁,d₀,k₀) system is a subshift of {0,1}ᶻ with run of 1 and 0 restricted to S=[d₁,k₁]₀=N∪{0} and S'=[d₀,k₀]₀ respectively. We extend this concept to the case when S and S' are arbitrary subsets of N₀ and we call it a (S,S')-gap shift. Moreover, for i=1,2, if Xᵢ is a synchronized system generated by Vᵢ={vⁱαᵢ:αᵢ vⁱαᵢ(Xᵢ),αᵢ vⁱ} where αᵢ is a synchronizing word for Xᵢ, then a natural generalization of (S,S')-gap shifts is a coded system Z generated by {v¹α₁ v²α₂:vⁱαᵢ∈ Vᵢ, i=1,2} and called the intertwined system. We investigate the dynamical properties of Z with respect to X₁ and X₂.
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