Abstract
In this paper, we introduce a three-way two-dimensional multicounter automaton which can be considered as an extension of an on-line multicounter machine to two dimensions, and investigate some of its properties. We first investigate the difference between the accepting powers of three-way and four-way two-dimensional multicounter automata, and between the accepting powers of nondeterministic and deterministic three-way two-dimensional multicounter automata. We then show that hierarchies can be obtained by varying the number of counters or the amount of space allowed, for classes of sets accepted by three-way two-dimensional multicounter automata. We finally examine closure properties under several operations. Input tapes in this paper are restricted to square ones.
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