1.3 Regular Expressions

















What's an Arithmetic Expression?
What are the operators and operands?

	2 * (4 - 8)

What type of object results from an Arithmetic Expression?


What's a Regular Expression?
What are the operators and operands?

	a*(a|b)

What type of object results from a Regular Expression?

















What's the Formal Definition of a Regular Expression?

	R is a Regular Expression if R is:

	1. a              (for some symbol a in the alphabet)
	2. epsilon
	3. empty-set
	4. (R1 | R2)      (for some Regular Expressions R1 and R2)
	5. (R1 R2)        (for some Regular Expressions R1 and R2)
	6. (R1*)          (for some Regular Expression R1)

What's the Language defined by a Regular Expression?

	L(a)               {a}
	L(epsilon)         {epsilon}
	L(empty-set)       {}
	L(R1 | R2)         L(R1) union L(R2)
	L(R1 R2)           L(R1) concat L(R2)
	L(R1*)             L(R1)*

















What's the order of operations in the expression?

	1 + 2 + 3 * 4


What's the order of operations in the expression?

	a | b c*


What's the Precedence of the Regular operators?

















Describe the language defined by the Regular Expression.

	ab*a
	a*b*
	a(a|b)*
	a(a|b)*b
	(a|b)*a(a|b)*
	(a|b)*(aa|bb)(a|b)*
	(a|b)*a(a|b)*a(a|b)*
	(a|b)*ab*ab*
	a* empty-set
	(empty-set)*
	a|empty-set
	a epsilon

















Write a Regular Expression for the language.
(w is a string of 0's and 1's)


	All strings except the empty string (1.18n)


	{ w | w has length >= 3 and its 3rd symbol is 0 } (1.18d)


	{ w | w contains an even number of 0s,
	      	or contains exactly two 1s } (1.18l)

















Classwork
(You may work with a partner.)

Write a Regular Expression for the language.
(w is a string of 0's and 1's)


	{ w | w starts with 0 and has odd length,
	       or starts with 1 and has even length } (1.18e)

















What are common applications of Regular Expressions?


	grep
	perl/python/php/ruby
	text editors