DFA Category 4: Specific length

 DFA accepts strings of exactly n characters. For Examples

  • Strings of length 3
  • Binary strings of length 5
  • Strings over {a, b} of length 2

DFA Example: 

Construct DFA, which accept all the string over alphabets ∑ {0,1} where the length of each string is exactly 2.


DFA Example: 

Construct DFA, which accept all the string over alphabets ∑ {0,1} where the length of each string is ≥ 2.


DFA Example: 

Construct DFA, which accept all the string over alphabets ∑ {0,1} where the length of each string is ≤ 2


DFA Example: 

Design a DFA over w {a,b}* such that length of “a” is greater or equals to 2 and there is no restriction over length of b.


DFA Example: 

Construct DFA, which accept all the string over alphabets ∑ {0,1} where the length of each string is EVEN.


DFA Example: 

Construct DFA, which accept all the string over alphabets ∑ {0,1} where the length of each string is ODD.


DFA Example:

Design a DFA with sigma ∑ = {0, 1}, accepts those strings that have an even number of “0’s” and an even number of “1’s”.

In Above DFA,

  • If state q1 becomes final instead of q0, the DFA will accept all those strings with Odd “0” and even “1”.
  • And if state q2 becomes final instead of q0, then the DFA will accept all those strings with even “0” and odd “1”.
  • And If state q3 becomes final instead of q0, then the DFA will accept all those strings with odd “0” and odd “1”.


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