We use results from communication complexity, both new and old ones, to prove lower bounds for unambiguous finite automata (UFAs). We show three results. $\textit{ Complement:}$ There is a language $L$ recognised by an $n$-state UFA such that the complement language $\overline{ L}$ requires NFAs with $n^{ \tilde{ \Omega}(\log n)}$ states. This improves on a lower bound by Raskin. $\textit{ Union:}$ There are languages $L_1$, $L_2$ recognised by $n$-state UFAs such that the union $L_1\cup L_2$ requires UFAs with $n^{ \tilde{ \Omega}(\log n)}$ states. $\textit{ Separation:}$ There is a language $L$ such that both $L$ and $\overline{ L}$ are recognised by $n$-state NFAs but such that $L$ requires UFAs with $n^{ \Omega(\log n)}$ states. This refutes a conjecture by Colcombet.
Categories: cs.FL cs.CC