(a) Give an encoding to integers of all deterministic finite-state automata (DFAs). [Here the alphabet of each such DFA is always taken from the set $\{0,1, \ldots\}$, and the states for each such DFA are always taken from the set $\left.\left\{q_{0}, q_{1}, \ldots\right\} .\right]$

(b) Show that the set of codes for which the corresponding DFA $D_{n}$ accepts a finite language is recursive. Moreover, if the language $\mathcal{L}\left(D_{n}\right)$ is finite, show that we can compute its size $\left|\mathcal{L}\left(D_{n}\right)\right|$ from $n$.