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Design DFA for language over {0,1} accepting strings with odd number of 1’s and even number of 0’s
A Deterministic Finite automaton (DFA) is a 5-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 1’s and even number of 0’s.
Solution
Design two separate machines for the two conditions over an alphabet Σ={0,1}:
DFA accepts only an odd number of 1’s.
DFA accepts only even number of 0’s.
Here,
s1 = start
s2=odd 1 or start 11
s3= starts 11 accepted and stay there
s4 = accept even 0, odd 1 and 0 1 0
s5=even 1, odd 0 and 0 1
s6=odd 1 odd 0
s7= odd 1 odd 0 start 010
s8=even 0 no 1
s0= odd 0 no 1
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