Prove that the DFA from Exercise $14\mathrm{.}3\mathrm{.}6$ in the book$1$ is minimal, either by running the

minimization algorithm on it or by showing that each pair of states is L$5-$distinguishable.

Solution:

$1$Exercise $14\mathrm{.}3\mathrm{.}6$: Let L$5$ be the set of binary strings that represent naturals that are divisible by five.

Design a DFA whose language is L$5.($It may help to look at Problem $14\mathrm{.}3\mathrm{.}3,$ which gives a DFA for the

similar language L$6.$