We consider input deterministic finite state transducers with infinite inputs and infinite outputs, and we consider the property of Borel normality on infinite words. When these transducers are given by a strongly connected set of states, and when the input is a Borel normal sequence, the output is an infinite word such that every word has a frequency given by a weighted automaton over the rationals. We prove that there is an algorithm that decides in cubic time whether an input deterministic transducer preserves normality.

中文翻译：

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通过换能器保持常态

我们考虑具有无限输入和无限输出的输入确定性有限状态转换器，并考虑无限词上的 Borel 正态性的性质。当这些换能器由一组强连接状态给出，并且当输入是一个 Borel 正规序列时，输出是一个无限的词，这样每个词都有一个由有理数上的加权自动机给出的频率。我们证明有一种算法可以在三次时间内决定输入确定性传感器是否保持正态性。