Lecture 3
Lecture 3
Lecture 3
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Proof (before the theorem!)<br />
A DFA has a finite number (say N) of states<br />
If a string w of length n>N is accepted then<br />
some state (say p) is revisited<br />
Let x be the prefix of w eaten on the way from q0 to p(first visit)<br />
Let y be the middle part of w eaten on the way from p (first visit) to p<br />
(second visit)<br />
Let z be the rest of w<br />
So w = xyz with |xy|≦ N, |y|>0<br />
xy i z is accepted by the DFA ∀i≧0<br />
Friday, February 8, 13
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