Three-dimensional alternating Turing machines with only universal states

We investigate several properties of three-dimensional alternating Turing machines whose input tapes are restricted to cubic ones. We first investigate the relationship between the classes of sets accepted by space-bounded and finitely leaf-size bounded five-way three-dimensional alternating Turing machines and the classes of sets which are finite intersections of sets accepted by space-bounded five-way three-dimensional nondeterministic Turing machines. Then, we investigate the accepting powers of three-dimensional alternating Turing machines with only universal states.