Construction Of DFA
Before you go through this article, make sure that you have gone through the previous article on Type01 Problems.
Type02 Problems
In Type02 problems, we will discuss the construction of DFA for languages consisting of strings starting with a particular substring.
Steps To Construct DFA
Following steps are followed to construct a DFA for Type02 problems
Step01:
 Determine the minimum number of states required in the DFA.
 Draw those states.
Use the following rule to determine the minimum number of states
RULECalculate the length of substring. All strings starting with ‘n’ length substring will always require minimum (n+2) states in the DFA. 
Step02:
 Decide the strings for which DFA will be constructed.
 The method for deciding the strings has been discussed in this Video.
Step03:
 Construct a DFA for the strings decided in Step02.
Remember the following rule while constructing the DFA
RULEWhile constructing a DFA,

Step04:
 Send all the left possible combinations to the dead state.
 Do not send the left possible combinations over the starting state.
PRACTICE PROBLEMS BASED ON CONSTRUCTION OF DFA
Problem01:
Draw a DFA for the language accepting strings starting with ‘ab’ over input alphabets ∑ = {a, b}
Solution
Regular expression for the given language = ab(a + b)*
Step01:
 All strings of the language starts with substring “ab”.
 So, length of substring = 2.
Thus, Minimum number of states required in the DFA = 2 + 2 = 4.
It suggests that minimized DFA will have 4 states.
Step02:
We will construct DFA for the following strings
 ab
 aba
 abab
Step03:
The required DFA is
Problem02:
Draw a DFA for the language accepting strings starting with ‘a’ over input alphabets ∑ = {a, b}
Solution
Regular expression for the given language = a(a + b)*
Step01:
 All strings of the language starts with substring “a”.
 So, length of substring = 1.
Thus, Minimum number of states required in the DFA = 1 + 2 = 3.
It suggests that minimized DFA will have 3 states.
Step02:
We will construct DFA for the following strings
 a
 aa
Step03:
The required DFA is
Problem03:
Draw a DFA for the language accepting strings starting with ‘101’ over input alphabets ∑ = {0, 1}
Solution
Regular expression for the given language = 101(0 + 1)*
Step01:
 All strings of the language starts with substring “101”.
 So, length of substring = 3.
Thus, Minimum number of states required in the DFA = 3 + 2 = 5.
It suggests that minimized DFA will have 5 states.
Step02:
We will construct DFA for the following strings
 101
 1011
 10110
 101101
Step03:
The required DFA is
Problem04:
Draw a DFA that accepts a language L over input alphabets ∑ = {0, 1} such that L is the set of all strings starting with ’00’.
Solution
Regular expression for the given language = 00(0 + 1)*
Step01:
 All strings of the language starts with substring “00”.
 So, length of substring = 2.
Thus, Minimum number of states required in the DFA = 2 + 2 = 4.
It suggests that minimized DFA will have 4 states.
Step02:
We will construct DFA for the following strings
 00
 000
 00000
Step03:
The required DFA is
Problem05:
Construct a DFA that accepts a language L over input alphabets ∑ = {a, b} such that L is the set of all strings starting with ‘aa’ or ‘bb’.
Solution
Regular expression for the given language = (aa + bb)(a + b)*
Step01:
Minimum number of states required in the DFA = 5.
It suggests that minimized DFA will have 5 states.
Step02:
We will construct DFA for the following strings
 aa
 aaa
 aaaa
 bb
 bbb
 bbbb
Step03:
The required DFA is
Problem06:
Construct a DFA that accepts a language L over input alphabets ∑ = {a, b} such that L is the set of all strings starting with ‘aba’.
Solution
Regular expression for the given language = aba(a + b)*
Step01:
 All strings of the language starts with substring “aba”.
 So, length of substring = 3.
Thus, Minimum number of states required in the DFA = 3 + 2 = 5.
It suggests that minimized DFA will have 5 states.
Step02:
We will construct DFA for the following strings
 aba
 abaa
 abaab
 abaaba
Step03:
The required DFA is
Also Read Converting DFA to Regular Expression
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