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DFA Example : Construct Minimal Finite Automata That Accept All The Strings Of 0’s And 1’s Such That Exactly Two 0’s

Construct Minimal Finite Automata That Accept All The Strings Of 0’s And 1’s

Such That

i) Exactly Two 0’s

ii) Almost Two 0’s

iii) Atleast Two 0’s

 

Solution

There Σ={0,1} // Here In The Place Of a,b The Input Alphabets Are a,b

 

i) Exactly Two 0’s

Possible Strings :- {00,001,01011,100,1001….} // String Should Contain Exactly Two 0’s

Small String Is 00

Here I Got The NFA, Now I’ll Convert This To DFA

I Need Exactly Two 0’s In Every String, I’ll Skip All 1’s

L={00,100,1010,11101101,101011….}

 

ii) Almost Two 0’s

L={ε,0,00,1010,1100,10101,……} // Infinite Strings

If Any Problem Contains ‘ε’ Then My Initial State Will Be My Final State

 

iii) At Least Two 0’s (Can Be At least Two 0’s And More Than Two 0’s)

L={00,000,001,00010101,…….}

 

 

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