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.
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