Abstract

In this paper, we investigate cyclic closure properties of several types of automata on a two-dimensional tape. It is shown that (1) the classes of sets accepted by two-dimensional finite automata, deterministic one-way parallel/sequential array automata, and two-dimensional deterministic on-line tessellation acceptors are not closed under row or column cyclic closure, and (2) the class of sets accepted by two-way parallel-sequential array automata is not closed under row cyclic closure.

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