Two-way one-counter automata accepting bounded languages

We show that languages such as <i>&Ltilde;</i> = {0<i><sup>n</sup></i>1<sup><i>n</i><sup>2</sup></sup>|<i>n</i>&ge; 1} and <i>&Lcirc;</i> = {0<i><sup>n</sup></i>1<sup>2<sup><i>n</i></sup></sup>|<i>n</i>&ge; 1} can be accepted by deterministic two-way one-counter automata.

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