We consider finite state non-deterministic but unambiguous transducers with infinite inputs and infinite outputs, and we consider the property of Borel normality of sequences of symbols. When these transducers are strongly connected, and when the input is a Borel normal sequence, the output is a sequence in which every block has a frequency given by a weighted automaton over the rationals. We provide an algorithm that decides in cubic time whether a unambiguous transducer preserves normality.

中文翻译：

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通过明确的换能器保持常态

我们考虑具有无限输入和无限输出的有限状态非确定性但明确的转换器，并且我们考虑符号序列的 Borel 正态性的性质。当这些转换器强连接时，并且当输入是一个 Borel 正规序列时，输出是一个序列，其中每个块都有一个由有理数上的加权自动机给出的频率。我们提供了一种算法，该算法以三次时间决定明确的换能器是否保持正态性。