Abstract
In this paper, we introduce a new model of acceptor on a three-dimensional pattern, called the time-bounded bottom-up pyramid cellular acceptor with three-dimensional layers whose input tapes are restricted to cubic ones (3-UPC AC), and investigate a relationship between the accepting powers of 3-UPCAc's and three-dimesional finite automata whose input tapes are restricted to cubic ones (3-FAc's). We first show that nondeterministic 3-UPCAc's are more powerful than nondeterministic 3-FAc's. We next show that O ((diameter) 2 × log diameter) time is sufficient for deterministic 3-U PC Ac's to simulate deterministic 3-FAc's, and that O ((diameter) 3) time is sufficient for deterministic 3-UPCAc's to simulate nondeterministic 3-FAc's. Finally, we show that Ω ((diameter) 2 × log diameter) time is necessary for nondeterministic 3-UPCAc's to simulate alternating 3-FAc's.
