regular language - Theory of computation GATE 2012 -

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4) consider set of strings on {0,1} in which, every sub string of 3 symbols has @ 2 zeros. examples, 001110 , 011001 in language, 100010 not. strings of length less 3 in language. partially completed dfa accepts language shown below.

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the missing arcs in dfa enter image description here

i preparing gate next year why have taken gate question regarding question appreciated.thank you!

answer option (d). first start language must not have 3 consecutive 0's. so,0 input 00 state must go dead state(q).and it's define in option (c) , (d). now,we have 2 option left. see state 10. in option (c) 0 input state 10 goes 10 only, it's loop , number 0's 10 it's stay on 10 , 10 final state it's accept language no of consecutive 0's , must not happen. left option (d) , (d) 0 input 10 goes state 00 , 1 more 0 00 it's goes dead state won't accept 3 consecutive 0's , our language want.and dfa should this.

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and done in option(d).sorry bad english.


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