1. 1 Some Properties of Regular Languages

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

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

4. 4 Example

5. 5 Union NFA for

6. 6 Example NFA for

7. 7 Concatenation NFA for

8. 8 Example NFA for

9. 9 Star Operation NFA for

10. 10 Example NFA for

11. 11 Regular Expressions

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

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

14. 14 Examples A regular expression: Not a regular expression:

15. 15 Languages of Regular Expressions : language of regular expression Example

16. 16 Definition For primitive regular expressions:

17. 17 Definition (continued) For regular expressions and

18. 18 Example Regular expression:

19. 19 Example Regular expression

20. 20 Example Regular expression

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

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

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

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

25. 25 Theorem Languages Generated by Regular Expressions Regular Languages