Chapter 3: Regular Language and RegularGrammar October 5, 2009 Chapter 3: Regular Language and Regular Grammar... Regular ExpressionRegular GrammarObjectives Regular Expression Regular E
Trang 1Chapter 3: Regular Language and Regular
Grammar
October 5, 2009
Chapter 3: Regular Language and Regular Grammar
Trang 2Regular ExpressionRegular Grammar
Objectives
Regular Expression
Regular Expression vs Regular Language
Regular Grammar
Regular Grammar vs Regular Language
Chapter 3: Regular Language and Regular Grammar
Trang 5Languages Associated with Regular Expressions
Each regular expression stands for a set of strings of symbols
r → L(r )
Chapter 3: Regular Language and Regular Grammar
Trang 6L((a + b.c) ∗ ) = {λ, a, bc, aa, abc, bca, bcbc, aaa, aabc, }
Chapter 3: Regular Language and Regular Grammar
Trang 8= {λ, a, aa, aaa, }.{a, b}
= {a, aa, aaa, , b, ab, aab, }
Chapter 3: Regular Language and Regular Grammar
Trang 13Equivalent Regular Expression
Definition
r 1 and r 2 are equivalent iff L(r 1 ) = L(r 2 )
Chapter 3: Regular Language and Regular Grammar
Trang 15Regular Languages
Definition
L is regular iff L = L(M) for some DFA M
Chapter 3: Regular Language and Regular Grammar
Trang 16Regular Expression
Regular Grammar
Regular Expression
Regular Expressions & Languages
Theorem 3.1 - Linz ’s book
Theorem
Chapter 3: Regular Language and Regular Grammar
Trang 17Regular Expressions & Languages
NFA that accepts {a}
Chapter 3: Regular Language and Regular Grammar
Trang 18Regular Expression
Regular Grammar
Regular Expression
Regular Expressions & Languages
Regular Expressions & Languages
λ
λ
λ
λ M(r 1 )
M(r 2 )
Chapter 3: Regular Language and Regular Grammar
Trang 19Regular Expressions & Languages
NFA that accepts L(r 1 r 2 )
Chapter 3: Regular Language and Regular Grammar
Trang 20Regular Expression
Regular Grammar
Regular Expression
Regular Expressions & Languages
Regular Expressions & Languages
NFA that accepts L(r 1 ∗ )
λ
λ M(r 1 )
Chapter 3: Regular Language and Regular Grammar
Trang 21Example 3.8
Chapter 3: Regular Language and Regular Grammar
Trang 22Regular Expression
Regular Grammar
Regular Expression
Regular Expressions & Languages
Theorem 3.2 - Linz ’s book
Trang 23Generalized Transition Graph
Trang 25Generation of Regular Expression
Trang 27Equivalent Regular Expression
Trang 28V: finite set of variables
Chapter 3: Regular Language and Regular Grammar
Trang 29Right-linear Grammar
Right-linear grammar:
G = (V , T , S , P) Productions are of the form:
Trang 34Chapter 3: Regular Language and Regular Grammar
Trang 35Theorem 3.3 - Linz ’s book
Theorem
Chapter 3: Regular Language and Regular Grammar
Trang 36Chapter 3: Regular Language and Regular Grammar
Trang 37Chapter 3: Regular Language and Regular Grammar
Trang 38Regular Expression
Regular Grammar
Regular Grammar
Regular Grammar & Language
Theorem 3.4 - Linz ’s book
Trang 41Theorem 3.5 - Linz ’s book
Trang 42Regular Expression
Regular Grammar
Regular Grammar
Regular Grammar & Language
Theorem 3.6 - Linz ’s book
Trang 43Exercises: 1, 4, 5, 6, 7, 13, 23 of Section 3.1 - Linzs book.
Exercises: 1, 3, 4, 7, 8, 9, 11, 13 of Section 3.2 - Linzs book.
Exercises: 1, 3, 5, 9, 13 of Section 3.3 - Linzs book.
Presentation: Pumping lemma and Christoph Neumann ’s paper.
Chapter 3: Regular Language and Regular Grammar