论文标题
$α$ - 免费语言的过渡属性，带有$α\ geq 2 $和$ k \ geq 3 $字母
Transition Property for $α$-Power Free Languages with $α\geq 2$ and $k\geq 3$ Letters
论文作者
论文摘要
1985年，Restivo和Salemi列出了五个有关无动力语言的问题。问题$ 4 $状态：给定$α$ - 无动力的单词$ u $和$ v $，确定是否有从$ u $过渡到$ v $。问题$ 5 $状态：给定$α$ - 无动力的单词$ u $和$ v $，如果存在，请找到一个过渡单词$ w $。 令$σ_k$表示用$ k $字母的字母。令$ l_ {k，α} $表示字母$σ_k$上的$α$ - 免费语言，其中$α$是有理数或合理的“具有$+$的数字”。如果$α$是“ $+$的数字”，则假设$ k \ geq 3 $和$α\ geq 2 $。如果$α$是“仅”一个数字，则假设$ k = 3 $和$α> 2 $或$ k> 3 $和$α\ geq 2 $。我们表明：如果$ u \ in l_ {k，α} $是$ l_ {k，α} $中的一个正确的可扩展单词，而l_ {k，α} $中的$ v \是$ l_ {k，α} $中的左扩展单词，则有一个$ w $ w $ w $ w $ $ w $ $ w $ a =我们还展示了$ w $一词的结构。
In 1985, Restivo and Salemi presented a list of five problems concerning power free languages. Problem $4$ states: Given $α$-power-free words $u$ and $v$, decide whether there is a transition from $u$ to $v$. Problem $5$ states: Given $α$-power-free words $u$ and $v$, find a transition word $w$, if it exists. Let $Σ_k$ denote an alphabet with $k$ letters. Let $L_{k,α}$ denote the $α$-power free language over the alphabet $Σ_k$, where $α$ is a rational number or a rational "number with $+$". If $α$ is a "number with $+$" then suppose $k\geq 3$ and $α\geq 2$. If $α$ is "only" a number then suppose $k=3$ and $α>2$ or $k>3$ and $α\geq 2$. We show that: If $u\in L_{k,α}$ is a right extendable word in $L_{k,α}$ and $v\in L_{k,α}$ is a left extendable word in $L_{k,α}$ then there is a (transition) word $w$ such that $uwv\in L_{k,α}$. We also show a construction of the word $w$.
