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# Design a DFA machine accepting odd numbers of 0’s or even numbers of 1’s

A Deterministic Finite automaton (DFA) is a five tuples

**M=(Q, Σ, δ,q0,F)**

Where,

- Q : Finite set called states.
- Σ : Finite set called alphabets.
- δ : Q × Σ → Q is the transition function.
- q0 ϵ Q is the start or initial state.
- F : Final or accept state.

## Problem

Construct a DFA machine accepting odd numbers of 0’s or even numbers of 1’s.

## Solution

Design two separate machines for the two conditions over an alphabet Σ={0,1} −

DFA accepting only odd number of 0’s

DFA accepting only even number of 1’s

**DFA accepting only odd number of 1’s over an alphabet Σ={0,1}**

The language L= {1,10,1110,1011,10101,100101,….}

**DFA accepting only even number of 1’s over an alphabet Σ={0,1}**

The language L= {11,101,11110,10111,101101,1001011,….}

Now merge two transition diagrams to generate a machine accepting odd number of 0’s or even number of 1’s

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