91Ó°ÊÓ

As per the above question, the procedure for Lemma 1.55 is used to convert regular expressions to nondeterministic finite automata. To, convert lemma 1.55 calculations is to follow, and count nondeterministic information is written below step-2 as below.

a. $\left(0+1\right)*000\left(0+1\right)*$

Consider the regular expression $R=\left(0∪1\right)*000\left(0∪1\right)*$.

Now, construct an NFA from this regular expression in the following procedure:

The regular expression of 0

The regular expression of 1

The regular expression of $(0∪1)$

The regular expression of $(0∪1)*$

The regular expression of 000

The regular expression of $(0∪1)*000(0∪1)*$

$\left(\left(00\right)*11+01\right)*$

Consider the regular expression $R=\left(\right(\left(00\right)*\left(11\right))∪(01\left)\right)*$ .

Now, construct the NFA from this regular expression in the following procedure:

The regular expression of 0

The regular expression of 1

The regular expression of 00

The regular expression of $\left(00\right)*$

The regular expression of 11

The regular expression of $\left(00\right)*11$

The regular expression of 01

The regular expression of$\left(\right(\left(00\right)*\left(11\right))∪(01\left)\right)$

The regular expression of $\left(\right(\left(00\right)*\left(11\right))∪(01\left)\right)*$

$âˆ\dots *=\mathrm{Î\mu }$

Let the normal expression $R=âˆ\dots *$ .

An unfilled format's closure is indeed an empty string. i.e., $âˆ\dots *=\left\{e\right\}$. The NFA for the regular expression is as follows: