Use the construction in the proof of Theorem 1.49 to give the state diagrams of NFAs recognizing the star of the languages described in

a. Exercise 1.6b

b. Exercise 1.6 j

c. Exercise 1.6m

THEOREM1.49

The class of regular languages is closed under the star operation.

Given that Theorem 1.49 , states that the class of regular languages are closed under star operation.

Consider the language $L_1=\left\{w|w\text{containsminimumthree}1\text{'}s\right\}$. Let $M_1$be the NFA that recognizes localid="1663238901072" $L_1$.

Consider that, localid="1663238860678" $L=L{*}_1$, let localid="1663238872432" $M$be the NFA that recognizes localid="1663238885929" $L$.

localid="1663238918361" $L_1=\left(0.1\right)*1\left(0.1\right)*1\left(0.1\right)*1\left(0.1\right)*$

The NFA localid="1663238930433" $M_1$that recognizes the language localid="1663238941815" $L_1$is as follows,

Therefore, the state diagram localid="1663239665261" $M$that recognizes localid="1663239651469" $L$is as follows.

Consider the language $L_1=\left\{w|w\text{includesminimumtwo}0\text{s}\text{andmostlyone}1\text{s}\right\}$.

Let $M_1$ be the NFA that recognizes the language $L_1$.

Let $L=L{*}_1$, and $M$be the NFA that recognizes $L$.

The state diagram of $M_1$is as follows,

Therefore the state diagram of $M$is as follows,

The language describes the empty string.

The state diagram of NFA that recognizes the empty string is as follows,