ON AN APPROACH TO FUNCTIONAL SPECIFICATION OF AUTOMATA SYSTEMS .3.

A language based on a logic of one-place predicates of an integral arg ument was described in Parts I and II [1, 2]. It was shown how that la nguage could be employed for the specification of deterministic automa ta superlexicographic functions. Nondeterministic automata X-Y-functio ns were presented as classes of specified deterministic automata X-Y-f unctions. It was also shown that all specified nondeterministic X-Y-fu nctions belong to the class PHI0(X, Y), which coincides with the class of X-Y-functions associated with all initial nondeterministic automat a of class K0(X, Y). The question naturally arises: which functions of PHI0(X, Y) can be X-Y-specified in the proposed language? An answer t o that question will be provided here; a subclass PHI1(X, Y) subset-or -equal-to PHI0(X, Y) of nondeterministic automata X-Y-functions will b e defined that coincides with the class of all such functions that can be X-Y-specified. As is class PHI0(X, Y), class PHI1(X, Y) is charact erized as the class of all automata X-Y-functions that are associated with automata of class K1(X, Y) subset-or-equal-to K0(X, Y). The defin itions, notation, and results of Parts I and II will be used extensive ly.