In this paper, we consider automata accepting irreducible sofic shifts, that is, strongly connected automata where each state is initial and final. We provide a characterization of unambiguity for finite words by means of measure of sets of infinite sequences labelling two runs. More precisely, we show that such an automaton is unambiguous, in the sense that no finite word labels two runs with the same starting state and the same ending state if and only if for each state, the set of infinite sequences labelling two runs starting from that state has measure zero.

中文翻译：

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度量理论视角下的歧义

在本文中，我们考虑自动机接受不可约的sofic位移，即每个状态均为初始和最终的强连接自动机。我们通过标记两个游程的无限序列集的度量来提供有限词的明确性。更确切地说，我们证明这种自动机是明确的，在某种意义上，当且仅当对于每个状态，标记两个游程的无限序列集从以下两个点开始时，没有有限字标记两个游程具有相同的起始状态和相同的终止状态该状态的度量为零。