Stochasticity of languages that can be recognized by two-sided finite probabilistic automata

We prove that with two-sided finite probabilistic automata only stochastic languages can be recognized, i.e., the capabilities of one-sided and two-sided finite probabilistic automata with a nonisolated point of intersection are identical with respect to recognition of languages. We give estimates for the increase in the number of states on passing from two-sided to one-sided automata that recognize the same language.