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FOSSACS
2008
Springer

Optimal Lower Bounds on Regular Expression Size Using Communication Complexity

8 years 11 months ago
Optimal Lower Bounds on Regular Expression Size Using Communication Complexity
The problem of converting deterministic finite automata into (short) regular expressions is considered. It is known that the required expression size is 2(n) in the worst case for infinite languages, and for finite languages it is n(log log n) and nO(log n) , if the alphabet size grows with the number of states n of the given automaton. A new lower bound method based on communication complexity for regular expression size is developed to show that the required size is indeed n(log n) . For constant alphabet size the best lower bound known to date is (n2 ), even when allowing infinite languages and nondeterministic finite automata. As the technique developed here works equally well for deterministic finite automata over binary alphabets, the lower bound is improved to n(log n) .
Hermann Gruber, Jan Johannsen
Added 26 Oct 2010
Updated 26 Oct 2010
Type Conference
Year 2008
Where FOSSACS
Authors Hermann Gruber, Jan Johannsen
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