1. Formal Language & Automata Theory
Shyamanta M Hazarika
Computer Sc. & Engineering
Tezpur University

2. Regular Language When we say: We are given a Regular Language We mean:
Language is in a standard
representation

3. Standard Representations
Regular Languages
DFAs
Regular
Grammars
NFAs
Regular
Expressions

4. Membership Question Question: Given regular language and string
how can we check if ?
Answer:
Take the DFA that accepts
and check if is accepted

5. Membership Question
DFA
DFA

6. Elementary Question Question: Given regular language how can we check
if is empty: ?
Take the DFA that accepts
Check if there is a path from
the initial state to a final state
Answer:

7. Elementary Question
DFA

8. Elementary Question Question: Given regular language
how can we check if
is finite?
Answer:
Take the DFA that accepts
Check if there is a walk with cycle
from the initial state to a final state

9. Elementary Question
DFA
is infinite
DFA
is finite

10. Elementary Question Question: Given regular languages and
how can we check if ?
Answer:
Find if

11. Elementary Question
and

12. Elementary Question or

13. Non-regular languages

14. Prove language is Not Regular
How can we prove that a language
is not regular?
Prove that there is no DFA that accepts
Problem: this is not easy to prove
Solution: Pumping Lemma !!!

15. The Pigeonhole Principle
pigeons
pigeonholes

16. The Pigeonhole Principle
A pigeonhole must
contain at least two pigeons

17. The Pigeonhole Principle
pigeons
pigeonholes

18. The Pigeonhole Principle
pigeons
pigeonholes
There is a pigeonhole
with at least 2 pigeons

19. Pigeonhole and DFA
DFA with states

20. Pigeonhole and DFA
In walks of strings:
no state
is repeated

21. Pigeonhole and DFA
a state
is repeated
In walks of strings:

22. Pigeonhole and DFA If the walk of string has length
then a state is repeated

23. Pigeonhole principle for any DFA
If in a walk of a string
transitions states of DFA
then a state is repeated