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On Regularity of Languages Generated by Copying Systems ; CU-CS-234-82

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TLDR
This note provides a sufficient condition for a copy language to be regular; an application of this condition is demonstrated.
Abstract
Abstract Let Σ be an arbitrary fixed alphabet. The direct copying relation (over Σ+) is a binary relation defined by: x copy y if and only if x = x1ux2 and y = x1uux2 for some words x1,x2,u where u is nonempty. The copying relation copy∗ is defined as the reflexive and transitive closure of copy. A copying system is an ordered pair G = (Σ, w) where w ϵΣ+; its language is L(G) = {zϵΣ + : w copy ∗ z} , it is referred to as a copy language. This note provides a sufficient condition for a copy language to be regular; an application of this condition is demonstrated.

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Language and Automata Theory and Applications, 14th International Conference LATA 2020, Milan, Italy, March 4–6, 2020, Proceedings

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References
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Avoidable patterns in strings of symbols

TL;DR: In this paper, it was shown that every Mh power-free word on n-letters is a subword of a maximal word of the same kind, and that all words of length at least 2 are avoidable.
Journal ArticleDOI

Uniformly growing k-th power-free homomorphisms

TL;DR: It is shown that there exist exponentially many square-free and cube-free strings of each length over these alphabets and arguments for the nonexistence of various RT(n)th power-free homomorphisms are provided.
Journal ArticleDOI

Sharp characterizations of squarefree morphisms

TL;DR: The following theorem is proved: “A semigroup morphism defined on a three letter alphabet is squarefree iff the images of the squarefree words of length 5 are squarefree”.