OUESTIONTWO $(2)$

Outline the formal description of the machines $M_1$ and $M_2$ in OUESTION ONE $(1)$

QUESTION THREE $(3)$

Assume that language $x$ is recognized by an NFA N$,$ and language $Y$ is the collection of strings not accepted by some DFA M$.$ Show that $x$@$Y$ is a regular language.

QUESTION FOUR $(4)$

A$.$ Show that if you add a finite set of strings to a regular language, the result is a regular language.

B$.$ Show that if you add a finite set of strings to a nonregular language, the result is a nonregular language.

QUESTION FIVE $(S)$

For the state diagram of the DFA $M$ below, give its formal definition as a $5-$tuple.With the following state diagrams of two DFAs, $M_1$ and $M_2,$ Provide the solution the questions

about each of these machines.

$M_1$

A$.$ What is the start state?

B$.$ What is the set of accept states?

C$.$ What sequence of states does the machine go through on input aabb $?$

D$.$ Does the machine accept the string aabb $?$

E$.$ Does the machine accept the string $?$