We introduce Probabilistic Regular Expressions (PRE), a probabilistic analogue of regular expressions denoting probabilistic languages in which every word is assigned a probability of being generated. We present and prove the completeness of an inference system for reasoning about probabilistic language equivalence of PRE based on Salomaa's axiomatisation of Kleene Algebra.

翻译：本文引入了概率正则表达式（PRE），即正则表达式的概率对应物，其表示的概率语言中每个单词都被赋予一个生成概率。我们提出并证明了一个基于Salomaa的Kleene代数公理化的推理系统，用于推理PRE的概率语言等价性的完备性。