Lec 4.ppt dsdsdd dd d r e rr e r er e r df

dwewe

1. 1

2. 2

3. 3

4. Courtesy Costas Busch -
RPI 4
Regular Expressions
Regular expressions describe regular
languages
Example:
 describes the language
*)( cba
 ,...,,,,,*, bcaabcaabcabca 

5. Courtesy Costas Busch -
RPI 5
Regular Expressions

1
1
21
21
*
r
r
rr
rr


Are regular expressions
2r1
rGiven regular expressions and

6. Courtesy Costas Busch -
RPI 6
Examples
  )(* ccba
A regular expression:
 baNot a regular expression:

7. Courtesy Costas Busch -
RPI 7
Languages of Regular
Expressions
: language of regular expression
Example
rL r
  ,...,,,,,*)( bcaabcaabcacbaL 

8. Courtesy Costas Busch -
RPI 8
Definition
For primitive regular expressions:


aaL
L
L





9. Courtesy Costas Busch -
RPI 9
Definition (continued)
For regular expressions and

1
r
2
r
 
2121
rLrLrrL 

2121 rLrLrrL 
**
11
rLrL 

11 rLrL 

10. Courtesy Costas Busch -
RPI 10
Example
Regular expression: *aba
 *abaL   *aLbaL
*aLbaL
 *aLbLaL
 *aba
 ,...,,,, aaaaaaba
 ,...,,,...,,, baababaaaaaa

11. Courtesy Costas Busch -
RPI 11
Example
Regular expression  bbabar  *
 ,...,,,,, bbbbaabbaabbarL

12. Courtesy Costas Busch -
RPI 12
Example
Regular expressionbbbaar **
 }0,:{
22
 mnbbarL
mn
If n, m >= 1

13. Courtesy Costas Busch -
RPI 13
Example
Regular expression *)10(00*)10( r
)(rL = { all strings with at least two consecutive 0 }

14. Courtesy Costas Busch -
RPI 14
Example
Regular expression )0(*)011( r
)(rL = { all strings without two consecutive 0 }

15. Courtesy Costas Busch -
RPI 15
Equivalent Regular Expressions
Definition:
 Regular expressions and

are equivalent if
1
r
2
r
)()(
21
rLrL

16. Courtesy Costas Busch -
RPI 16
Example
 L= { all strings without two consecutive 0 }
)0(*)011(
1
r
)0(*1)0(**)011*1(
2
 r
LrLrL  )()(
21
1
r
2
rand
are equivalent
regular expr.