91Ó°ÊÓ

Use Theorem 1.45 which states the union of regular languages to construct state diagrams of NFA of the given languages.

Consider the given languages ,

$$\begin{gathered} L_1=\left\{w\right|w \text{²õ³Ù²¹°ù³Ù·É¾±³Ù³ó1 a²Ô»å´Ú¾±²Ô¾±²õ³ó·É¾±³Ù³ó a} 0\} \\ {L}_2=\{w|w u\text{singatleastthree1s}\}\text{on}∑=\left\{0,1\right\} \end{gathered}$$.

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

The union of the language can be defined as, $L=L_1∪L_2$and $M$be the NFA that recognizes $L$.

The state diagram of $M_1$is as follows,

The state diagram of M₂ is as follows,

Therefore, the state diagram of M is as follows,

Consider the languages,

$L_1=\left\{w\right|w\text{containsthesubstring}0101i.e,w=x0101y\text{forsome}x\text{and}y\}on∑=\{0,1\}$

$L_1=\left\{w\right|w\text{doesn'tcontainthesubstring}110\}\text{on}∑=\{0,1\}$.

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

The union of two languages is , $L=L_1∪L_2$ and it is recognized by the NFA $M$.

The state diagram of $M_1$is as follows,

The state diagram of $M_2$is as follows,

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