Provide an NFA with almost six states for the following language
L={w/w contains an even number of 0’s or exactly 1’s
Answers
Here is an NFA (Non-Deterministic Finite Automaton) with six states that recognizes the language L = {w | w contains an even number of 0s, or exactly two 1s}:
State: q0
Transitions:
On input symbol 0: Transition to q1
On input symbol 1: Transition to q2
State: q1
Transitions:
On input symbol 0: Transition to q0
On input symbol 1: Transition to q3
State: q2
Transitions:
On input symbol 0: Transition to q2
On input symbol 1: Transition to q4
State: q3
Transitions:
On input symbol 0: Transition to q3
On input symbol 1: Transition to q5
State: q4
Transitions:
On input symbol 0: Transition to q4
On input symbol 1: Transition to q5
State: q5
Transitions:
On input symbol 0: Transition to q5
On input symbol 1: Transition to q5
State q0 is the initial state, and q5 is the only accepting (final) state.
This NFA will accept strings where the number of 0s is even or there are exactly two 1s. States q1 and q4 are intermediate states used to keep track of the number of 0s encountered.
States q2, q3, and q5 are used to account for the condition of exactly two 1s.
Please note that this NFA has exactly six states, as requested.
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