Lower Bounds on Unambiguous Automata Complementation and Separation via Communication Complexity
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^Ω̃(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^Ω(log n) states, refuting a conjecture by Colcombet on separation.
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