Exercise $2\mathrm{.}2\mathrm{.}10$ : Consider the DFA with the following transition table:

$01$

$->$ A A B

$*$B B A

Informally describe the language accepted by this DFA, and prove by induction

on the length of an input string that your description is correct. H in t When

setting up the inductive hypothesis, it is wise to make a statement about what

inputs get you to each state, not just what inputs get you to the accepting

state.