下推尺寸
Pushdown dimension
摘要：
本文发展了下推维理论，并探讨了它与有限状态维的关系。对于所有序列，下推维数由有限状态维数平凡地限制，因为下推赌徒可以模拟任何有限状态赌徒。我们证明了对于任意有理数0 < d < 1，存在一个有限状态维数为d的序列，其下推维数至多为d/2。这建立了一个定量的模拟众所周知的事实，即下推自动机决定严格更多的语言比有限自动机。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
