(Solved): (20 points) You can build a transition table for any deterministic finite automaton. This table ha ...

(20 points) You can build a transition table for any deterministic finite automaton. This table has as many rows as states, and as many columns as symbols in the alphabet that the strings are made out of (plus a column listing whether the state is a final state). Entry T \( \mathrm{Ti}][\mathrm{x}] \) shows what the next state would be if you're in state \( i \) and see symbol \( j \). Consider the DFA below for the regular expression \( \left(y \mid\left(x x^{*}\right)\right) y \) : The transition table for this is: Note that we don't indicate a transition to the error state. Instead, we just mark the transition as - . We saw an example of this kind of transition table when building the subset construction. (a) (10 points) Draw the transition table for the following DFA: (b) (10 points) Draw the DFA corresponding to the following transition table (pay attention to the symbols in the alphabet!):