The Search for a Definition of Partition Pair for Stochastic Automata

The concept of "partition pair" is important for the decomposition of deterministic machines. The theory of stochastic machines would be enhanced with a suitable generalization. The definition of partition pairs presented by Bacon fails in that it does not reduce to the deterministic definition for a stochastic machine which is actually deterministic. A natural definition of partition pair is presented using probability distributions rather than states.