Necessary Spaces For Seven-Way Four-Dimensional Turing Machines To Simulate Four-Dimensional One-Marker Automata

We think that recently, due to the advances in many application areas such as motion image processing, computer animation, and so on, it is very useful for analyzing computational complexity of multi-dimensional information processing to explicate the properties of four-dimensional automata, i.e., three-dimensional automata with the time axis. As far as we know, there is no investigation about four-dimensional automata. Then, in 2002, we first introduced four-dimensional finite automata in the world. In 2003, we investigated four-dimensional alternating Turing machines. In 2015, we show the sufficient spaces for four-dimensional Turing machines to simulate four-dimensional one-marker automata. In this paper, we continue the investigations, and deal with the necessary spaces for four-dimensional Turing machines to simulate four-dimensional one-marker automata.