a) Give an NFA accepting the set of strings {0, 1}^* such that two 00 s are separated by a string whose length is 4i, for some i 0.

b) Convert the NFA defined by (q₀, a) = {q₀, q₁}, (q₁, b) = {q₁, q₂}, (q₂, a) = {q₂}, (q₀, ) = {q₁, q₂} with initial state q₀ and final state q₂ into an equivalent DFA. Assume the input alphabets are {a, b}.