Finitely Nonstationary Nondeterministic Automata with Random Input

Properties of generalized finitely nonstationary nondeterministic automata with an additional random input over a Boolean lattice are considered which are related to the definition of the class of languages represented by such automaton models. New notions of an elementary nondeterministic automatic structure with a random input, of a generalized finitely nonstationary nondeterministic automaton with a random input, of the generalized mapping induced by such an automaton, and of a generalized language represented by such an automaton are introduced. A number of statements substantiating synthesis for any given generalized finitely nonstationary nondeterministic automaton with a random input of an abstract probabilistic finite automaton equivalent to the given one relative to the represented generalized language probabilistic language of the stationary abstract probabilistic finite automaton. The number of states of the synthesized probabilistic automaton is estimated and a synthesis algorithm is developed in detail and illustrated by an example.