We study the computational power of parsing expression grammars (PEGs). We begin by constructing PEGs with unexpected behaviour, and surprising new examples of languages with PEGs, including the language of palindromes whose length is a power of two, and a binary-counting language. We then propose a new computational model, the scaffolding automaton, and prove that it exactly characterises the computational power of parsing expression grammars (PEGs). Several consequences will follow from this characterisation: (1) we show that PEGs are computationally “universal”, in a certain sense, which implies the existence of a PEG for a P-complete language; (2) we show that there can be no pumping lemma for PEGs; and (3) we show that PEGs are strictly more powerful than online Turing machines which do $o(n/{(\log n)}^2)$ steps of computation per input symbol.

我们研究了解析表达语法（PEG）的计算能力。我们首先构建具有意外行为的PEG，并使用PEG编写令人惊讶的语言新实例，包括长度为2的幂的回文所用的语言以及一种二进制计数语言。然后，我们提出了一个新的计算模型，即脚手架自动机，并证明它准确地表征了解析表达语法（PEG）的计算能力。这种表征将产生以下几种后果：（1）从某种意义上讲，我们证明PEG在计算上是“通用的”，这意味着P完全语言存在PEG。（2）我们证明PEG不会存在泵抽引物。（3）我们证明PEG绝对比在线Turing机器功能强大$Ø（ñ/{（\mathrm{日志}ñ）}^2）$ 每个输入符号的计算步骤。