# Intersection process of two DFAs

Prerequisite – Design a Finite automata

Let’s understand the intersection of two DFA with an example.

Designing a DFA for the set of string over {0, 1} such that it ends with 01 and has even number 0f 1’s.

There two desired language will be formed:

L_{1}= {01, 001, 101, 0101, 1001, 1101, ....} L_{2}= {11, 011, 101, 110, 0011, 1100, .....}

L = L_{1}and L_{2}= L_{1}∩ L_{2}

**State Transition Diagram for the language L _{1} :**

This is a DFA for language L

_{1}

It accepts all the string that accept 01 at end.

**State Transition Diagram for the language L _{2} :**

This is a DFA for language L

_{2}

It accepts all the string that accept with even number of 1’s.

**State Transition Diagram of L _{1} ∩ L_{2} : **

Intersection of L

_{1}and L

_{2}can be explained by language that a string over {0, 1} accept such that it ends with 01 and has even number of 1’s.

L = L_{1}∩ L_{2}= {1001, 0101, 01001, 10001, ....}

Thus as we see that L_{1} and L_{2} have been combined through intersection process and this final DFA accept all the language that has even number of 1’s and is ending with 01.