State Minimization

Construct an equivalent deterministic finite state automaton with the minimum number of states. $($You

also have to show the equivalence classes generated in each iteration of the minimization algorithm $($

corresponding to the relations $-={?}_0,-={?}_1,$dots $).)$

a$)$

b$)$

Non$-$Regular Languages

Using the Pumping Lemma for Regular Languages, show that the following languages over the

alphabet $=\{a,b\}$ are not regular.

a$)|)$:$\}$ contains the symbol a twice as many times as the symbol $\{$:$b\}$

b$)L=\{{}^R|=(abbb{)}^{**}\}$