We propose a new approach for universal lossless text compression, based on grammar compression. In the literature, a target string $T$ has been compressed as a context-free grammar $G$ in Chomsky normal form satisfying $L(G) = \{T\}$. Such a grammar is often called a \emph{straight-line program} (SLP). In this paper, we consider a probabilistic grammar $G$ that generates $T$, but not necessarily as a unique element of $L(G)$. In order to recover the original text $T$ unambiguously, we keep both the grammar $G$ and the derivation tree of $T$ from the start symbol in $G$, in compressed form. We show some simple evidence that our proposal is indeed more efficient than SLPs for certain texts, both from theoretical and practical points of view.

中文翻译：

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使用概率上下文无关语法进行语法压缩

我们提出了一种基于语法压缩的通用无损文本压缩新方法。在文献中，目标字符串 $T$ 已被压缩为满足 $L(G) = \{T\}$ 的乔姆斯基范式中的上下文无关文法 $G$。这种文法通常被称为 \emph{straight-line program} (SLP)。在本文中，我们考虑生成 $T$ 的概率文法 $G$，但不一定是 $L(G)$ 的唯一元素。为了明确地恢复原始文本 $T$，我们将语法 $G$ 和 $T$ 的派生树以压缩形式保留在 $G$ 中的起始符号中。我们展示了一些简单的证据，从理论和实践的角度来看，我们的提议确实比某些文本的 SLP 更有效。