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• W2082934005 abstract "Nondeterministic finite automata (NFA) with at most one accepting computation on every input string are known as unambiguous finite automata (UFA). This paper considers UFAs over a one-letter alphabet, and determines the exact number of states in DFAs needed to represent unary languages recognized by n -state UFAs in terms of a new number-theoretic function g ˜ . The growth rate of g ˜ ( n ) , and therefore of the UFA–DFA tradeoff, is estimated as e Θ ( n ln 2 n 3 ) . The conversion of an n -state unary NFA to a UFA requires UFAs with g ( n ) + O ( n 2 ) = e ( 1 + o ( 1 ) ) n ln n states, where g ( n ) is the greatest order of a permutation of n elements, known as Landauʼs function. In addition, it is shown that representing the complement of n -state unary UFAs requires UFAs with at least n 2 − o ( 1 ) states in the worst case, while the Kleene star requires up to exactly ( n − 1 ) 2 + 1 states." @default.
• W2082934005 created "2016-06-24" @default.
• W2082934005 creator A5005683089 @default.
• W2082934005 date "2012-03-01" @default.
• W2082934005 modified "2023-09-25" @default.
• W2082934005 title "Unambiguous finite automata over a unary alphabet" @default.
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• W2082934005 doi "https://doi.org/10.1016/j.ic.2012.01.003" @default.
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