Abstract
Several properties of two-dimensional alternating Turing machines are investigated. The first part of this paper investigates the relationship between the classes of sets accepted by space-bounded and finitely leaf-size bounded three-way two-dimensional alternating Turing machines and the classes of sets which are finite intersections of sets accepted by space-bounded three-way two-dimensional nondeterministic Turing machines. The second part of this paper investigates the accepting power and closure properties (under Boolean operations) of two-dimensional alternating Turing machines with only universal states.
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