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Pushdown dimension

David Doty·Jared Nichols
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Abstract

This paper develops the theory of pushdown dimension and explores its relationship with finite-state dimension. Pushdown dimension is trivially bounded above by finite-state dimension for all sequences, since a pushdown gambler can simulate any finite-state gambler. We show that for every rational 0 < d < 1, there exists a sequence with finite-state dimension d whose pushdown dimension is at most d/2. This establishes a quantitative analogue of the well-known fact that pushdown automata decide strictly more languages than finite automata.

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David Doty, Jared Nichols. 2005-05-27. Pushdown dimension. https://arxiv.org/abs/cs/0504047

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