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Unambiguous non-deterministic finite automata have intermediate expressivepower and succinctness between deterministic and non-deterministic automata. Ithas been conjectured that every unambiguous non-deterministic one-way finiteautomaton (1UFA) recognizing some language L can be converted into a 1UFArecognizing the complement of the original language L with polynomial increasein the number of states. We disprove this conjecture by presenting a family of1UFAs on a single-letter alphabet such that recognizing the complements of thecorresponding languages requires superpolynomial increase in the number ofstates even for generic non-deterministic one-way finite automata. We also notethat both the languages and their complements can be recognized by sweepingdeterministic automata with a linear increase in the number of states.

A superpolynomial lower bound for the size of non-deterministic complement of an unambiguous automaton