1. CSE322 PROPERTIES OF REGULAR LANGUAGES
Lecture #12

2. Closure properties of Regular set
Set Union
Concatenation
Closure(iteration)
Transpose
Set intersection
Complementation

3. Properties of Regular Languages

4. For regular languages and
we will prove that:
Union:
Are regular
Languages
Concatenation:
Star:
Reversal:
Complement:
Intersection:

5. Union: Concatenation: Star: Reversal: Complement: Intersection:
We say: Regular languages are closed under
Union:
Concatenation:
Star:
Reversal:
Complement:
Intersection:

6. Regular language Regular language NFA NFA Single aceepting state
Single accepting state
NFA

7. Example

8. Union
NFA for

9. Example
NFA for

10. Concatenation
NFA for

11. Example
NFA for

12. Star Operation
NFA for

13. Example
NFA for

14. Reverse
NFA for
Homework 2

15. Complement
Homework 2

16. Intersection
regular
We show
regular
regular

17. DeMorgan’s Law:
regular

18. Example
regular
regular
regular

19. Construct a new FA that accepts
Another Proof for Intersection Closure
Machine
Machine FA
for FA
for
Construct a new FA that accepts
simulates in parallel and

20. States in
State in
State in

21. FA FA
transition
transition FA
transition

22. FA FA
initial state
initial state FA
Initial state

23. FA FA
accept state
accept states FA
accept states
Both constituents must be accepting states

24. Example:

25. Automaton for intersection

26. simulates in parallel and
accepts string
if and only if
accepts string and
accepts string