Abstract
This paper estimates the number of states in an unambiguous finite automaton (UFA) that is sufficient and in the worst case necessary to simulate an n-state two-way deterministic finite automaton (2DFA) and an n-state two-way unambiguous finite automaton (2UFA). It is proved that a 2UFA with n states can be transformed to a UFA with fewer than 2n⋅n! states. On the other hand, for every n, there is a language recognized by an n-state 2DFA that requires a UFA with at least Ω((2+1)2n⋅n−1)=Ω(5.828n) states. The latter result is obtained as a lower bound on the rank of a certain matrix.
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