2.1 Write regular expression for the following character sets, or reasons why no regular expression can be written: a. All strings of lowercase letters that begin and end in a. b. All strings of lowercase letters that either begin or end in a both) c. All strings of digits that contain no leading zeros d. All strings of digits that represent even numbers
2.1 Write regular expression for the following character sets, or reasons why no regular expression can be written: a. All strings of lowercase letters that begin and end in a. b. All strings of lowercase letters that either begin or end in a both) c. All strings of digits that contain no leading zeros d. All strings of digits that represent even numbers
Computer Networking: A Top-Down Approach (7th Edition)
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Author:James Kurose, Keith Ross
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Chapter1: Computer Networks And The Internet
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![### Regular Expression Exercise
#### 2.1 Write a regular expression for the following character sets, or provide reasons why no regular expression can be written:
a. **All strings of lowercase letters that begin and end in `a`.**
b. **All strings of lowercase letters that either begin or end in `a` (or both).**
c. **All strings of digits that contain no leading zeros.**
d. **All strings of digits that represent even numbers.**
#### Explanation:
**a**:
For strings that begin and end with `a`, the regular expression can be:
```
^a[a-z]*a$
```
Here, `^` asserts the position at the start of a line, `a` matches the start character, `[a-z]*` matches zero or more lowercase letters, and `a$` matches the last character and asserts position at the end of a line.
**b**:
For strings that either begin or end with `a` (or both), the regular expression can be:
```
(^a[a-z]*$)|(^[a-z]*a$)
```
This combines two conditions: strings that begin with `a` or those that end with `a`.
**c**:
For strings of digits that contain no leading zeros, the regular expression can be:
```
^[1-9][0-9]*$
```
Here, `^` asserts the position at the start of a line, `[1-9]` matches any digit from 1 to 9 (ensuring no leading zero), and `[0-9]*` matches zero or more digits.
**d**:
For strings of digits that represent even numbers, the regular expression can be:
```
^[0-9]*[02468]$
```
This matches any sequence of digits ending in 0, 2, 4, 6, or 8, which represent even numbers.
### Notes:
- For part c, a string containing only "0" is not specified, but typically, "0" would be considered a special case.
- The regular expressions are written considering that `^` and `$` are used to assert the start and end of lines, respectively.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fce5cea56-9cd3-471d-b739-11e3ad279d5e%2F76953808-e715-4756-8731-57c8c67c2a99%2Fpnwr2bc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Regular Expression Exercise
#### 2.1 Write a regular expression for the following character sets, or provide reasons why no regular expression can be written:
a. **All strings of lowercase letters that begin and end in `a`.**
b. **All strings of lowercase letters that either begin or end in `a` (or both).**
c. **All strings of digits that contain no leading zeros.**
d. **All strings of digits that represent even numbers.**
#### Explanation:
**a**:
For strings that begin and end with `a`, the regular expression can be:
```
^a[a-z]*a$
```
Here, `^` asserts the position at the start of a line, `a` matches the start character, `[a-z]*` matches zero or more lowercase letters, and `a$` matches the last character and asserts position at the end of a line.
**b**:
For strings that either begin or end with `a` (or both), the regular expression can be:
```
(^a[a-z]*$)|(^[a-z]*a$)
```
This combines two conditions: strings that begin with `a` or those that end with `a`.
**c**:
For strings of digits that contain no leading zeros, the regular expression can be:
```
^[1-9][0-9]*$
```
Here, `^` asserts the position at the start of a line, `[1-9]` matches any digit from 1 to 9 (ensuring no leading zero), and `[0-9]*` matches zero or more digits.
**d**:
For strings of digits that represent even numbers, the regular expression can be:
```
^[0-9]*[02468]$
```
This matches any sequence of digits ending in 0, 2, 4, 6, or 8, which represent even numbers.
### Notes:
- For part c, a string containing only "0" is not specified, but typically, "0" would be considered a special case.
- The regular expressions are written considering that `^` and `$` are used to assert the start and end of lines, respectively.
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