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Marker versus inkdot on four-dimensional tapes

A multi-marker automaton is a finite automaton which keeps marks as pebbles in the finite control, and cannot rewrite any input symbols but can make marks on its input with the restriction that only a bounded number of these marks can exist at any given time. An improvement of picture recognizability of the finite automaton is the reason why the multi-marker automaton was introduced. On the other hand, a multi-inkdot automaton is a conventional automaton capable of dropping an inkdot on a given input tape for a landmark, but unable to further pick it up. Due to the advances in many application areas such as moving image processing, computer animation, and so on, it has become increasingly apparent that the study of four-dimensional pattern processing has been of crucial importance. Thus, we think that the study of four-dimensional automata as a computational model of four-dimensional pattern processing has also been meaningful. This paper deals with marker versus inkdot over four-dimensional input tapes, and investigates some properties.