平衡直线程序
Balancing Straight-Line Programs
摘要：
它示出，上下文上下文无关文法的大小$m$，产生一个单一的字符串$w$（这样的语法也被称为一个字符串直线程序），可以在线性时间转换成上下文上下文无关文法的语法$w$的大小$\mathcal{O}(m)$，其独特的推导树有深度$\mathcal{O}(\log |w|)$。这解决了基于语法的压缩领域中的一个公开问题。类似的结果显示两种形式主义基于语法的树压缩：顶dags和森林直线程序。这些平衡结果都是从一个单一的Meta定理推导出来的，该元定理指出，具有一定有限基性质的代数上的代数电路的深度可以减少到$\mathcal{O}(\log n)$，而成本是常数乘法大小的增加。这里，$n$指的是电路展开（或解开）的大小。
英文摘要：
It is shown that a context-free grammar of size $m$ that produces a single string $w$ (such a grammar is also called a string straight-line program) can be transformed in linear time into a context-free grammar for $w$ of size $\mathcal{O}(m)$, whose unique derivation tree has depth $\mathcal{O}(\log |w|)$. This solves an open problem in the area of grammar-based compression. Similar results are shown for two formalism for grammar-based tree compression: top dags and forest straight-line programs. These balancing results are all deduced from a single meta theorem stating that the depth of an algebraic circuit over an algebra with a certain finite base property can be reduced to $\mathcal{O}(\log n)$ with the cost of a constant multiplicative size increase. Here, $n$ refers to the size of the unfolding (or unravelling) of the circuit.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
