Transactions of the Institute of Systems, Control and Information Engineers
Online ISSN : 2185-811X
Print ISSN : 1342-5668
ISSN-L : 1342-5668
A Relationship between the Accepting Powers of Three-Dimensional Finite Automata and Time-Bounded Bottom-Up Pyramid Cellular Acceptors with Three-Dimensional Layers
Makoto SAKAMOTOShigehisa NOGAMIKatsushi INOUEMichio KONO
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2004 Volume 17 Issue 10 Pages 451-458

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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.

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