We use results from communication complexity, both new and old ones, to prove lower bounds for problems on unambiguous finite automata (UFAs). We show: (1) Complementing UFAs with $n$ states requires in general at least $n^{\tilde{\Omega}(\log n)}$ states, improving on a bound by Raskin. (2) There are languages $L_n$ such that both $L_n$ and its complement are recognized by NFAs with $n$ states but any UFA that recognizes $L_n$ requires $n^{\Omega(\log n)}$ states, refuting a conjecture by Colcombet on separation.

中文翻译：

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通过通信复杂性的无歧义自动机补充和分离的下限

我们使用新旧通信复杂度的结果来证明无歧义有限自动机 (UFA) 问题的下界。我们表明：（1）用 $n$ 状态补充 UFA 通常需要至少 $n^{\tilde{\Omega}(\log n)}$ 状态，改进了 Raskin 的界限。(2) 有语言 $L_n$ 使得 $L_n$ 及其补码都被具有 $n$ 状态的 NFA 识别，但是任何识别 $L_n$ 的 UFA 都需要 $n^{\Omega(\log n)}$ 状态，驳斥了 Colcombet 关于分离的猜想。