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（PRE），它是正则表达式的概率模拟，用于表示概率语言，其中每个词都被赋予一个生成概率。我们基于Salomaa对Kleene代数的公理化，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。