We say that a language $L$ is \emph{constantly growing} if there is a constant $c$ such that for every word $u\in L$ there is a word $v\in L$ with $\vert u\vert<\vert v\vert\leq c+\vert u\vert$. We say that a language $L$ is \emph{geometrically growing} if there is a constant $c$ such that for every word $u\in L$ there is a word $v\in L$ with $\vert u\vert<\vert v\vert\leq c\vert u\vert$. Given two infinite languages $L_1,L_2$, we say that $L_1$ \emph{dissects} $L_2$ if $\vert L_2\setminus L_1\vert=\infty$ and $\vert L_1\cap L_2\vert=\infty$. In 2013, it was shown that for every constantly growing language $L$ there is a regular language $R$ such that $R$ dissects $L$. In the current article we show how to dissect a geometrically growing language by a homomorphic image of intersection of two context-free languages. Consider three alphabets $\Gamma$, $\Sigma$, and $\Theta$ such that $\vert \Sigma\vert=1$ and $\vert \Theta\vert=4$. We prove that there are context-free languages $M_1,M_2\subseteq \Theta^*$, an erasing alphabetical homomorphism $\pi:\Theta^*\rightarrow \Sigma^*$, and a nonerasing alphabetical homomorphism $\varphi : \Gamma^*\rightarrow \Sigma^*$ such that: If $L\subseteq \Gamma^*$ is a geometrically growing language then there is a regular language $R\subseteq \Theta^*$ such that $\varphi^{-1}\left(\pi\left(R\cap M_1\cap M_2\right)\right)$ dissects the language $L$.

翻译：我们称语言$L$为\emph{恒定增长}，若存在常数$c$使得对每个单词$u\in L$，存在单词$v\in L$满足$\vert u\vert<\vert v\vert\leq c+\vert u\vert$。称语言$L$为\emph{几何增长}，若存在常数$c$使得对每个单词$u\in L$，存在单词$v\in L$满足$\vert u\vert<\vert v\vert\leq c\vert u\vert$。给定两个无限语言$L_1,L_2$，若$\vert L_2\setminus L_1\vert=\infty$且$\vert L_1\cap L_2\vert=\infty$，则称$L_1$\emph{分割}$L_2$。2013年已证明：对每个恒定增长语言$L$，存在正则语言$R$使得$R$分割$L$。本文展示如何通过两个上下文无关语言交集的同态像来分割几何增长语言。考虑三个字母表$\Gamma$、$\Sigma$和$\Theta$，其中$\vert \Sigma\vert=1$且$\vert \Theta\vert=4$。我们证明存在上下文无关语言$M_1,M_2\subseteq \Theta^*$、擦除字母同态$\pi:\Theta^*\rightarrow \Sigma^*$以及非擦除字母同态$\varphi : \Gamma^*\rightarrow \Sigma^*$，使得：若$L\subseteq \Gamma^*$为几何增长语言，则存在正则语言$R\subseteq \Theta^*$，使得$\varphi^{-1}\left(\pi\left(R\cap M_1\cap M_2\right)\right)$分割语言$L$。