1 Some Properties of Regular Languages

2 Properties Concatenation:Star: Union: Are regular Languages For regular languages and

3 We Say: Regular languages are closed under Concatenation:Star: Union:

4 Example

5 Union NFA for

6 Example NFA for

7 Concatenation NFA for

8 Example NFA for

9 Star Operation NFA for

10 Example NFA for

11 Regular Expressions

12 Regular Expressions Regular expressions describe regular languages Example: describes the language

13 Recursive Definition Are regular expressions Primitive regular expressions: Given regular expressions and

14 Examples A regular expression: Not a regular expression:

15 Languages of Regular Expressions : language of regular expression Example

16 Definition For primitive regular expressions:

17 Definition (continued) For regular expressions and

18 Example Regular expression:

19 Example Regular expression

20 Example Regular expression

21 Example Regular expression = { all strings with at least two consecutive 0 }

22 Example Regular expression = { all strings without two consecutive 0 }

23 Equivalent Regular Expressions Definition: Regular expressions and are equivalent if

24 Example = { all strings without two consecutive 0 } and are equivalent regular expr.

25 Theorem Languages Generated by Regular Expressions Regular Languages