ISI 2015 PCB C4 B

Question

Draw a 4-state DFA for the language $L \subseteq$ {a,b}* , L = {x : the number of time ab appears in x is even}

Answer 1

note: 2nd state just after initial state is also final state.

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Comments

This will accept a string with single b*. Is that okay?

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yes string contain no ab menas contain 0 ab which is even.
one mistake in above figure, 2nd state will also be final state.

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Also error in the 3rd state. Should be a self loop on input b

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yes right

Answer 2

Summering the answers...here is the one

Answer 3

The above DFA accepts all strings having even number of ab

Comments

it will also accept only {ba , a ,bba, b , bb... }

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yes sir because in  ba , a, bba the number of times ab occur is zero which is also even .

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correct change this comment to ans