Lower Bounds on Unambiguous Automata Complementation and Separation via Communication Complexity
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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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