A Relationship between the Accepting Powers of Three-Dimensional Finite Automata and Time-Bounded Bottom-Up Pyramid Cellular Acceptors with Three-Dimensional Layers

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 A^C), and investigate a relationship between the accepting powers of 3-UPCA^c's and three-dimesional finite automata whose input tapes are restricted to cubic ones (3-FA^c's). We first show that nondeterministic 3-UPCA^c'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 A^c's to simulate deterministic 3-FAc's, and that O ((diameter) ³) time is sufficient for deterministic 3-UPCA^c's to simulate nondeterministic 3-FA^c's. Finally, we show that Ω ((diameter) ² × log diameter) time is necessary for nondeterministic 3-UPCAc's to simulate alternating 3-FA^c's.