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arXiv · 1602.03510

Describtion of normal basis of boundary algebras and factor languages of small growth

A. Ya. Belov·A. L. Chernyatiev
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Abstract

Let $A$ be an algebra with fixed set of generators $a_1,\dots,a_s$. $V_A(n)$ be dimension of the space, generated by worlds of length $\le n$ over $a_i$, $T_A(n)=V_A(n)-V_A(n-1)$. If $T_A(n)<\mbox{Const}$, algebra $A$ is a {\it boundary algebra}. We describe a normal basis of boundary algebras, i.e. algebras with small growth. Let $\cal L$ be a factor language over alphabet $\cal A$. {\it Growth function} $T_{\cal L}(n)$ is number of subwords $\cal L$ of degree $n$. We describe factor languages of small growth such that $T_{\cal L}(n)\le n+\mbox{const}$.

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A. Ya. Belov, A. L. Chernyatiev. 2016-02-10. Describtion of normal basis of boundary algebras and factor languages of small growth. https://doi.org/10.4213/mzm11408

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