Construction Of DFA
In this article, we will learn the construction of DFA.
Type01 Problems
In Type01 problems, we will discuss the construction of DFA for languages consisting of strings ending with a particular substring.
Steps To Construct DFA
Following steps are followed to construct a DFA for Type01 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 ending with ‘n’ length substring will always require minimum (n+1) 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 starting state.
 Do not send the left possible combinations over the dead state.
PRACTICE PROBLEMS BASED ON CONSTRUCTION OF DFA
Problem01:
Draw a DFA for the language accepting strings ending with ’01’ over input alphabets ∑ = {0, 1}
Solution
Regular expression for the given language = (0 + 1)*01
Step01:
 All strings of the language ends with substring “01”.
 So, length of substring = 2.
Thus, Minimum number of states required in the DFA = 2 + 1 = 3.
It suggests that minimized DFA will have 3 states.
Step02:
We will construct DFA for the following strings
 01
 001
 0101
Step03:
The required DFA is
Problem02:
Draw a DFA for the language accepting strings ending with ‘abb’ over input alphabets ∑ = {a, b}
Solution
Regular expression for the given language = (a + b)*abb
Step01:
 All strings of the language ends with substring “abb”.
 So, length of substring = 3.
Thus, Minimum number of states required in the DFA = 3 + 1 = 4.
It suggests that minimized DFA will have 4 states.
Step02:
We will construct DFA for the following strings
 abb
 aabb
 ababb
 abbabb
Step03:
The required DFA is
Problem03:
Draw a DFA for the language accepting strings ending with ‘abba’ over input alphabets ∑ = {a, b}
Solution
Regular expression for the given language = (a + b)*abba
Step01:
 All strings of the language ends with substring “abba”.
 So, length of substring = 4.
Thus, Minimum number of states required in the DFA = 4 + 1 = 5.
It suggests that minimized DFA will have 5 states.
Step02:
We will construct DFA for the following strings
 abba
 aabba
 ababba
 abbabba
 abbaabba
Step03:
The required DFA is
Problem04:
Draw a DFA for the language accepting strings ending with ‘0011’ over input alphabets ∑ = {0, 1}
Solution
Regular expression for the given language = (0 + 1)*0011
Step01:
 All strings of the language ends with substring “0011”.
 So, length of substring = 4.
Thus, Minimum number of states required in the DFA = 4 + 1 = 5.
It suggests that minimized DFA will have 5 states.
Step02:
We will construct DFA for the following strings
 0011
 00011
 000011
 0010011
 00110011
Step03:
The required DFA is
Also Read Converting DFA to Regular Expression
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