Remarks on Four-Dimensional Alternating Turing Machines with Only Universal States

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During the past about forty years, many types of two- or three-dimensional automata have been proposed and investigated the properties of them as the computational model of pattern processing. On the other hand, recently, due to the advances in many application areas such as computer animation, motion image processing, and so on, the study of three-dimensional pattern processing with the time axis has been of crucial importance. Thus, we think that it is very useful for analyzing computation of three-dimensional pattern processing with the time axis to explicate the properties of four-dimensional automata. In this paper, we deal with four-dimensional alternating Turing machines, and investigate several accepting powers of four-dimensional alternating Turing machines which each sidelength of each input tape is equivalent.
2009-09-30