Give state diagrams of NFAs with the specified number of states recognizing each of the following languages. In all parts, the alphabet is $\left\{0,1\right\}$.

a. The language$\left\{w|w\text{endswith}00\right\}$with three states

b.The language of Exercise 1.6c with five states

c.The language of Exercise 1.6l with six states

d. The language $\left\{0\right\}$ with two states

e. The language $\mathbf{0}\mathbf{*}\mathbf{1}\mathbf{*}{\mathbf{0}}^{\mathbf{+}}$ with three states

f. The language$\mathbf{1}\mathbf{*}\left({001}^{+}\right)\mathbf{*}$ with three states

g. The language$\left\{\epsilon \right\}$with one state

h. The language $\mathbf{0}\mathbf{*}$with one state

A state diagram is used in computer science and related fields to describe the behavior of system. A state diagram represents the transition from one state to another based on the inputs given.

Considering the given language, relatively limited automata must have five states that take strings from all across the letters. Let M be the NFA that recognizes L . The state diagram of M is as follows :

Consider the languages,

$$\begin{gathered} L_1=\left\{w\right|w\text{\hspace{0.05em}containsanevennumberof}0s\} \\ {L}_2=\{w|w\text{\hspace{0.05em}contains\hspace{0.05em}exactly\hspace{0.05em}two} 1\text{'}s\} \end{gathered}$$

Let $M_1\text{and}{M}_2$be the NFAs that recognizes the languages $L_1\text{and}{L}_2$respectively.

The language Lis defined as $L=L_1\cup L_2$ and the NFA Mrecognizes the language L.

The state diagram of M₁ is as follows,

The state diagram of M₂ is as follows,

Therefore, the state diagram of M is as follows,

Considering the given language, relatively limited automata must have two states that take strings from all across the letters. Let M be the NFA that recognizes L . The state diagram of M is as follows :

Considering the given language, relatively limited automata must have three states that take strings from all across the letters. Let M be the NFA that recognizes L . The state diagram of M is as follows :

Considering the given language, relatively limited automata must have three states that take strings from all across the letters. Let M be the NFA that recognizes L . The state diagram of M is as follows :

Considering the given language, relatively limited automata must have one state that take strings from all across the letters. Let M be the NFA that recognizes L . The state diagram of M is as follows :

Considering the given language, relatively limited automata must have one state that take strings from all across the letters. Let M be the NFA that recognizes L . The state diagram of M is as follows :