Abstract
This paper investigates a relationship among the accepting powers of time-bounded bottom-up pyramid cellular acceptors, nondeterministic two-dimensional on-line tessellation acceptors, and two-dimensional finite automata. Let UPCA denote a bottom-up pyramid cellular acceptor. Then we show that (1) nondeterministic UPCAs which operate in O(diameter) time can simulate nondeterministic two-dimensional on-line tessellation acceptors, and thus such nondeterministic UPCAs are more powerful than nondeterministic two-dimensional finite automata, (2) O(diameter× log diameter) time is necessary for deterministic UPCAs to simulate deterministic two-dimensional finite automata, and (3) O((diameter) 2) time is necessary for deterministic UPCAs to simulate nondeterministic two-dimensional finite automata.
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