1. CSE 340 Recitation Week 3 : Sept 1st – 7th Regular Expressions
Questions
Project 2
Regular Expressions
Valid Syntax
Using REs to Define a Language
Evaluating whether “????” is in a Language
RE v. MATH
Application of REs -- Tokens

2. Questions?
Current Project
Homework
Lecture
Other?

3. Project 2 Project 2 is due 9/9/16 FRIDAY before 11:59pm
Part 1 (30 points)
Debug buggy program
Common mistakes
Extract with $tar –xzvf <filename>
Included test script, runs the 6 test cases in test.sh
Use diff command to create patch :
$ diff -uwB buggy_program.c good_program.c > fix_bugs.patch

4. Project 2 – Part 2 Part 2 – Lexer + Linked List
Will use getToken() to get input from STDIN
getToken() returns token_type enum
ID, NUM, IF, WHILE, DO, THEN, PRINT
Global variables set by getToken()
T_type – same as returned by getToken()
current_token – contains token value or blank
token_length – length of string stored in current_token
line – the line number of current_token

5. Project 2 – Part 2 Part 2 – Lexer + Linked List
ID and NUM tokens stored into Linked List
Need to store Token Type, Token Value, Line number
Will need to print output out in reverse (one option might be to use a doubly linked list)
Token Type
Value
Line #
Next
Token Type
Value
Line #
Next
Token Type
Value
Line #
Next
Next
Next
Next
Previous
Previous
Previous

6. Project 2 – Part 2 Part 2 – Lexer + Linked List
Must use a Linked List data structure
Must create reversed output from list, will not receive full credit if output to string to and print string in reverse.
Token Type
Value
Line #
Next
Token Type
Value
Line #
Next
Token Type
Value
Line #
Next
Next
Next
Next
Previous
Previous
Previous

7. Project 2 – Part 2
Part 2 – Lexer + Linked List

8. Project 2 – Part 2 Part 2 – Lexer + Linked List Standard Output
Standard Input
Standard Output

9. Project 2 – Part 2 Part 2 – Lexer + Linked List Evaluation Testing
A test script that runs multiple test cases is provided
Details on test scripts in project document
Evaluation
Graded on whether the test cases are passed
Must use a C-Style linked list (a struct with a self-referential field)
CANNOT USE the STL

10. Regular Expressions Valid Syntax for REs
Definition of Languages using REs
Is“????”  Language (i.e. L(RE) or {})
RE v MATH

11. Valid Syntax for REs A syntactically valid regular expression has ∅ 𝜺
a, where a is an element of the alphabet
R1 | R2, where R1 and R2 are regular expressions
R1 . R2, where R1 and R2 are regular expressions
(R), where R is a regular expression
R*, where R is a regular expression

12. Valid Syntax for REs Given:  = {a, b, c, d, 1, 2 , 3, 4}
Are these valid REs?
Z = a | b | c
Y = (1 | 2 | 3)*
X = (Z | 𝜺)
W = ((1.2 | 2.3 ) 4*)
V = X.Z.Y.X.Y ∅ 𝜺
a, where a is an element of the alphabet
R1 | R2, where R1 and R2 are regular expressions
R1 . R2, where R1 and R2 are regular expressions
(R), where R is a regular expression
R*, where R is a regular expression

13. Valid Syntax for REs Given:  = {a, b, c, d, 1, 2 , 3, 4}
Are these valid REs?
Z = a | b | c
Y = (1 | 2 | 3)*
X = (Z | 𝜺)
W = ((1.2 | 2.3 ).4*)
V = X.Z.Y.X.Y ∅ 𝜺
a, where a is an element of the alphabet
R1 | R2, where R1 and R2 are regular expressions
R1 . R2, where R1 and R2 are regular expressions
(R), where R is a regular expression
R*, where R is a regular expression

14. Definition of Languages using REs
What is 𝛴?
What is 𝛴*?
Given :  = {a, b, c, d, 1, 2, 3}
Is “dddddddddddddddcccccccccccccccaaaaaaaaaaaaaaaa aaaaaaaaaaaaaa bbbbbbbbbbbbaaaaaaaa ”  𝛴*?

15. Definition of Languages using REs
What is 𝛴?
What is 𝛴*?
Given :  = {a, b, c, d, 1, 2, 3}
Is “dddddddddddddddcccccccccccccccaaaaaaaaaaaaaaaa aaaaaaaaaaaaaa bbbbbbbbbbbbaaaaaaaa ”  𝛴*?
YES

16. Definition of Languages using REs
What is a Language?
A Language is a subSET of 𝛴*
i.e., L  𝛴*
How do we describe that subset?
Using REs

17. Definition of Languages using REs
 = {a, b, c, d, 1, 2, 3}
Z = a | b | c
Y = (1 | 2 | 3)*
X = (Z | 𝜺)
W = (2.3.4*) | 𝜺
V = X.Y.Z.W.X.Y
L(V) = {…}

18. Definition of Languages using REs
L(V) = {…}
This uses the V regular expression to define the subset 𝛴*
Thus, L(V)  𝛴*
 = {a, b, c, d, 1, 2, 3}
Z = a | b | c
Y = (1 | 2 | 3)*
X = (Z | 𝜺)
W = (2.3.4*) | 𝜺
V = X.Y.Z.W.X.Y

19. Definition of Languages using REs
What are some examples of strings that are in L(V)?
L(V) = {a1a234a3, 1aa3, …}
Is “a1a234a3”  𝛴*
YES
 = {a, b, c, d, 1, 2, 3}
Z = a | b | c
Y = (1 | 2 | 3)*
X = (Z | 𝜺)
W = (2.3.4*) | 𝜺
V = X.Y.Z.W.X.Y

20. Is“????”  Language (i.e. L(RE) or {})
Does L(V) contain: a
b123
ab123ab123
ab123c8 a
312d333
Why is it not in L(V)?
 = {a, b, c, d, 1, 2, 3, 4}
Z = a | b | c
Y = (1 | 2 | 3)*
X = (Z | 𝜺)
W = (2.3.4*) | 𝜺
V = X.Y.Z.W.X.Y √ X

21. Is“????”  Language (i.e. L(RE) or {})
What must L(V) always contain?
a, b, or c
Why?
b/c of RE Z
 = {a, b, c, d, 1, 2, 3}
Z = a | b | c
Y = (1 | 2 | 3)*
X = (Z | 𝜺)
W = (2.3.4*) | 𝜺
V = X.Y.Z.W.X.Y

22. EPSILON Is this a valid set? Is this a valid regular expression?
= {a, b, c, d, 𝜺, |, .}
Is this a valid regular expression?
Z=a.b.c .𝜺.𝜺
Is 𝜺 the character represented by the alphabet or the RE representation of empty string?

23. EPSILON Usually we will define like this, for clarity.
= {a, b, c, d, \𝜺, \|, \.}
Is this a valid regular expression?
Z=a.b.c.\ 𝜺 . 𝜺
“abc𝜺”  L(Z)?

24. EPSILON = {a, b, c, d} Is this a valid regular expression?
Z=a.b.c.(a|𝜺).b.c
What strings are in L(Z)?
Is “abc𝜺”  L(Z)?

25. EPSILON √ X = {a, b, c, d} Is this a valid regular expression?
Z=a.b.c.(a|𝜺).b.c
What is in the language?
L(Z) = {abcabc, abcbc}
Are these strings in L(Z)?
“abcbc”  L(Z)?
“abc𝜺bc”  L(Z)?
WHY? √ X

26. RE v. Math A regular expression defines a subset of 𝛴* L(∅) = ∅
L(a) = {a}
L(R1 | R2) = L(R1) ∪ L(R2)
L(R1 . R2) = L(R1) . L(R2)
L((R)) = L(R)
L(R*) = L(R*) = ∪i≥0 Li(R) ∅ 𝜺
a, where a is an element of the alphabet
R1 | R2, where R1 and R2 are regular expressions
R1 . R2, where R1 and R2 are regular expressions
(R), where R is a regular expression
R*, where R is a regular expression

27. RE v. Math
Operator Precedence Just like Math () () ^ * . . | similar to +

28. RE v. Math
L(R1 . R2) = L(R1) . L(R2) For two sets A and B of strings: A . B = {xy : x ∈ A and y ∈ B}

29. RE v. Math
 = {a, b, c, d, 1, 2, 3}
Z = a | b | c
X = (Z | 𝜺)
A . B = {xy : x ∈ A and y ∈ B}
Example: L(X.Z) = L(X).L(Z) = L(Z|𝜺).L(a|b|c) = (L(Z) U L(𝜺)).(L(a) U L(b) U L(c))= (L(a) U L(b) U L(c) U L(𝜺)).(L(a) U L(b) U L(c))= ({a} U {b} U {c} U {𝜺}) . ({a} U {b} U {c}) = {a, b, c, 𝜺}.{a,b,c} = {aa, ab, ac, ba, bb, bc, ca, cb, cc, a, b, c}

30. RE v. Math L(R*) = ∪i≥0 Li(R), where L0(R) = {𝜺} Definition
Li(R) = Li-1(R) . L(R)
L(R*) = ∪i≥0 (Li-1(R) . L(R))

31. RE v. Math L(R*) = ∪i≥0 Li(R), where L0(R) = {𝜺} L (R*) = {𝜺} ∪ L(R) ∪
L(R) . L( R) . L(R) . L(R) …

32. RE v. Math Example: L(Y) L((1 | 2 | 3)*) = {𝜺} U L(1|2|3) U
L(1|2|3). L(1|2|3) U
L(1|2|3). L(1|2|3) . L(1|2|3) U …
L(1|2|3) = L(1) U L(2) U L(3) = {1} U {2} U {3} = {1,2,3}
 = {a, b, c, d, 1, 2, 3}
Y = (1 | 2 | 3)*
L(R1 | R2) = L(R1) ∪ L(R2)
L(R1 . R2) = L(R1) . L(R2)
A . B = {xy : x ∈ A and y ∈ B}
L(R*) = ∪i≥0 Li(R)
where L0(R) = {𝜺}