Session-20.pdf - Minimization of DFA Algorithm Begin 1 For...

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Minimization of DFA: Algorithm: Begin 1) For p in F and q in Q F do mark(p,q); 2) For each pair of distinct states (p,q) in F * F or (Q-F) * (Q-F) do 3) If input symbols a,( δ (p,a), δ(q,a) ) is marked then Begin 4) Mark (p,q); 5) Recursively mark all unmarked pairs on the list for (p,q) and on the lists of other pairs that are marked at this step. End Else /* no pair ( δ (p,a), δ (q,a)) is marked */ 6) For all input symbol α do 7) Put (p,q) on the list for ( δ (p,a), δ (q,a)) unless δ (p,a)= δ (q,a) End 1) Construct minimum state finite automata for the following finite automata
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b X c X X d X X X e X X X f X X X X g X X X X X X h X X X X X X a b c d e f g First place X in the entries corresponding to one final and one non-final state i.e., we place X on the entries (a,c),(b,c),(c,d),(c,e),(c,f),(c,g),(c,h). For (a,b): 0 1 a b f b g c (a,b) are not equivalent on 1 so mark at (a,b) For (a,d): 0 1 a b d c (a,d) are not equivalent on 0. So mark at (a,d) For (a,e): 0 1 a b f e h f
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For (a,f): 0 1 a b f f c g (a,f) are not equivalent on 0. So mark at (a,f) For (a,g): 0 1 a b f g g e For (a,h):
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