Decidability, Arithmetic Subsequences and Eigenvalues of Morphic Subshifts
نویسندگان
چکیده
منابع مشابه
Extremal words in morphic subshifts
Given an infinite word x over an alphabet A, a letter b occurring in x, and a total order σ on A, we call the smallest word with respect to σ starting with b in the shift orbit closure of x an extremal word of x. In this paper we consider the extremal words of morphic words. If x = g(fω(a)) for some morphisms f and g, we give two simple conditions on f and g that guarantees that all extremal wo...
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Let A be a finite alphabet and f : A → A be a morphism with an iterative fixed point f(α), where α ∈ A. Consider the subshift (X , T ), where X is the shift orbit closure of f(α) and T : X → X is the shift map. Let S be a finite alphabet that is in bijective correspondence via a mapping c with the set of nonempty suffixes of the images f(a) for a ∈ A. Let S ⊂ S be the set of infinite words s = ...
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We study finite state transduction of automatic and morphic sequences. Dekking [4] proved that morphic sequences are closed under transduction and in particular morphic images. We present a simple proof of this fact, and use the construction in the proof to show that non-erasing transductions preserve a condition called α-substitutivity. Roughly, a sequence is α-substitutive if the sequence can...
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ژورنال
عنوان ژورنال: Bulletin of the Belgian Mathematical Society - Simon Stevin
سال: 2019
ISSN: 1370-1444
DOI: 10.36045/bbms/1576206359