Abstract
In this paper, we investigate several properties of on-line n-bounded multicounter machines. An on-line n-bounded multicounter machine is an on-line multicounter machine in space n which can test whether or not the contents of each counter is equal to the input length. It is shown that 1. (1) there is a set accepted by a deterministic on-line n-bounded 1-counter machine but not by any deterministic on-line multicounter machine in space n, 2. (2) there is a set accepted by a nondeterministic on-line n-bounded 1-counter machine but not by any deterministic on-line n-bounded multicounter machine, 3. (3) there is a set accepted by a deterministic on-line n-bounded ( k + 1)-counter machine ( k ⩾ 1) but not by any nondeterministic on-line n-bounded k-counter machine, and 4. (4) the class of sets accepted by deterministic on-line n-bounded k-counter machines ( k ⩾ 1) is not closed under union, intersection, concatenation, Kleene closure, reversal, or e-free homomorphism.
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