A Prime Decomposition of Probabilistic Automata
Representation Theory
2015-03-06 v1
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.
Cite
@article{arxiv.1503.01502,
title = {A Prime Decomposition of Probabilistic Automata},
author = {Gunnar Carlsson and Jun Yu},
journal= {arXiv preprint arXiv:1503.01502},
year = {2015}
}