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：我们引入概率正则表达式（Probabilistic Regular Expressions, PRE），它是正则表达式的概率类比，表示每个单词被赋予生成概率的概率性语言。我们基于Salomaa的Kleene代数公理化系统，提出并证明了一个用于推理PRE概率语言等价性的推理系统的完备性。