A Completeness Theorem for Probabilistic Regular Expressions

ACM/IEEE Symposium on Logic in Computer Science（2023）

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Abstract

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.

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