Question

Consider the dfa with initial state q₀, final state q₂ and

δ(q₀,a) = q₂ δ(q₀,b) = q₂
δ(q₁,a) = q₂ δ(q₁,b) = q₂
δ(q₂,a) = q₃ δ(q₂,b) = q₃
δ(q₃,a) = q₃ δ(q₀,b) = q₁
Find a minimal equivalent dfa.

Answer 1

To find a minimal equivalent DFA, eliminate unreachable states and merge equivalent states. In this DFA, remove q₁. Merge q₀ and q₂ to get the final minimal equivalent DFA with q₀ (initial and final) and q₃.

Step-by-step explanation:

To find a minimal equivalent DFA, we need to eliminate any unreachable states and merge equivalent states. In this DFA, the state q₁ is unreachable, so we can remove it. Now, we can start merging equivalent states. Since q₀ and q₂ have the same transitions and q₀ is the initial state, we can combine them into a single state. The final minimal equivalent DFA has two states: q₀ (initial and final) and q₃.