A probabilistic Büchi automaton PBA is defined. The probabilistic language (L, p) as defined by the PBA is defined. A decomposition theorem similar to the classical Krohn-Rhodes theorem, but for PBA is proved.

A probabilistic Büchi automaton PBA is defined. The probabilistic language (L, p) as defined by the PBA is defined. A decomposition theorem similar to the classical Krohn-Rhodes theorem, but for PBA is proved.