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arXiv · 1503.01502

A Prime Decomposition of Probabilistic Automata

Gunnar Carlsson·Jun Yu
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Abstract

A definition of a probabilistic automaton is formulated in which its prime decomposition follows as a direct consequence of Krohn-Rhodes theorem. We first characterize the local structure of probabilistic automata. The prime decomposition is presented as a framework to study the global structure of probabilistic automata. We prove that the representation theory of a probabilistic automaton is determined by that of the finite groups in its holonomy decomposition.

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Gunnar Carlsson, Jun Yu. 2015-03-04. A Prime Decomposition of Probabilistic Automata. https://arxiv.org/abs/1503.01502

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