This document contains lecture notes on regular expressions (RE) from Dr. Hussien Sharaf. It defines REs and their notation. RE rules are presented, along with examples of using REs to describe sets of strings with certain properties, such as having at least two 'a's. Students are assigned exercises on REs and implementing an email validator in Python. The deadline is February 28th and TA help is available for the next three days.

1. WELCOME TO A
JOURNEY TO
CS419
Dr. Hussien Sharaf
Computer Science Department
dr.sharaf@from-masr.com

2. DEFINITION OF A LANAGUAGE “L”
∑ is the set of alphabets
*
1. Let ∑ ={x}, Then L = ∑
*
In RE, we write x
*
2. Let ∑ ={x, y}, Then L = ∑
*
In RE, we write (x+y)
3. Kleene’s star “*” means any combination of
letters of length zero or more.
Note: Please study the appendix at the end of
the lecture
Dr. Hussien M. Sharaf
2

3. RE RULES
Given an alphabet ∑, the set of regular expressions is
defined by the following rules.
1.
2.
For every letter in ∑, the letter written in bold is a
regular expression. Λ- lamda or ε-epsilon is a
regular expression. Λ or ε means an empty letter.
If r1 and r2 are regular expressions, then so are:
1.
2.
3.
4.
(r1)
r1 r2
r1+r2
r1* and also r2*
NOTE 1: r1+ is not a RE
NOTE 2: spaces are ignored as long as they are not included in ∑
3.
Nothing else is a regular expression.
Dr. Hussien M. Sharaf
3

4. RE-10.1
Example
∑ ={a, b}, What does L describe?
*
*
- L = (a+b) a(a+b)

Any string of a's and b's
Any string of a's and b's
Single a
- Give examples for words in L
{a ab aab bab abb …..}
Dr. Hussien M. Sharaf
4

5. RE-10.2
abbaab can be parsed in 3 ways
a bbaab
Λ a bbaab
Dr. Hussien M. Sharaf
abba a b
abb a ab
abb
a
ab
abba
a
b
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6. RE-11
Example
∑ ={a, b}
- Formally describe all words with at least two a's.
1) L = b*ab*a(a + b)*
 Start with a jungle of b's (or no b's) until we find
the first a, then more b's (or no b's), then the
second a, then we finish up with anything.
- Give examples for words in L
{abbbabb aaaaa bbbabbbbabab…..}

Dr. Hussien M. Sharaf
6

7. RE-12
Example
∑ ={a, b}
- Formally describe all words with exactly two a's.
1) L = b*ab*ab*
- Give examples for words in L
{aab, baba, and bbbabbbab …..}
 To make the word aab, we let the first and second
b* become Λ and the last becomes b

Dr. Hussien M. Sharaf
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8. RE-13.1
Example
∑ ={a, b}
- Formally describe all words with at least
one a and at least one b.
1) L = (a + b)*a(a + b)* b(a + b)*

= (anything) a(anything) b(anything)
But (a+b)*a(a+b)*b(a+b)* expresses all words except
words of the form some b’s (at least one) followed by
some a’s (at least one).
bb*aa*
Dr. Hussien M. Sharaf
8

9. RE-13.1
2) L =(a+b)*a(a+b)*b(a+b)* + bb*aa*
Thus: (a+b)*a(a+b)*b(a+b)* + (a+b)*b(a+b)*a(a+b)*
= (a+b)*a(a+b)*b(a+b)* + bb*aa*

Notice that it is necessary to write bb*aa*
because b*a* will admit words we do not
want, such as aaa.
Does this imply that
(a+b)*b(a+b)*a(a+b)*= bb*aa*??
False Left side includes the word aba, which
the
expression on the right side does not.
Dr. Hussien M. Sharaf
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10. ASSIGNMENTS
1.
2.
3.
[One week] Solve Compilers-Sheet_0General.pdf
[One week] Solve Compilers_Sheet_1_RE.pdf
[Two weeks] Implement an email validator
using Python.
a.
b.
c.
Build a GUI using python Tkinter.
The GUI must include at least two labels, a TextBox
and a Button.
The user is given a message on a label stating
whether the email is a valid email or not.
Dr. Hussien M. Sharaf
10

11. DEADLINE
Thursday 28th of Feb is the deadline.
 No excuses.
 Don’t wait until last day.
 TAs can help you to the highest limit
within the next 3 days.

Dr. Hussien M. Sharaf
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12. THANKS
Dr. Hussien M. Sharaf
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