A short presentation to share knowledge about topic Decidability of Theory of Automata Course. To make people to be aware how to know which formal languages are decidable and why...!

1. DECIDABILITY
By:
M.Daniyal Ashfaq (2013-CS-51)
Shahrukh Mahesar (2013-CS-32)
M.Waleed Aslam (2013-CS-14)
Sagar Kumar (2013-CS-39)
Section : 4A
To:
Mehwish Wahid
Theory of Automata & Formal Languages
Department of Computer Science
Sir Syed University of Engineering & Technology Karachi

2. Contents
Introduction
Advantages
Decidability in Automata
Types:
◦ Decidable
◦ Semi-Decidable
◦ Undecidable
Decidable Problems
◦ For C.F.L
◦ For F.A
Undecidable Problems
◦ For T.M
References

3. Introduction
An Effective solution to a problem that has
“Yes” or “No” answer.
Having Decision procedure is known as
Decidable.

4. Advantages
Determined Goal.
Strong Procedure.
More Accurate.
Time Saving.

5. Decidability in Automata
An algorithm, determining the validity of a
given input.
Divided into three parts:
 Decidable
 Semi-decidable
 Un-decidable

6. Decidable
Existance of an effecive algorithm
Ability to determine whether an input is
acceptable or not.

7. Semidecidable
Existance of an Algorithm, having effectiveness
in theory
Sometimes fail to determine exact answer
practically.

8. Undecidable
Existing no effective algorithm
Solutions can not be determined

9. Decidable
Problems(C.F.L)
Emptiness?
Finiteness?
Membership?

10. Decidable
Problems(C.F.L)
Solution:-
Emptiness:
Convert CFG into CNF.
 Finiteness:
Apply Pumping Lemma.
Membership:
Apply CYK algorithm on CNF form.
 Hence CFL is Decidable.

11. Decidable Problems(F.A)
Is the same Language accepted by two
different F.As?
Is the same Language defined by two different
R.Es?

12. Decidable Problems(F.A)
Solution:-
 Convert both F.A’s into Regular Expression.
 Get a minimum word Accepted by both.
 Hence FA is Decidable.

13. Undecidable
Problem(T.M)
The Halting Problem?
Null Words?
Emptiness?
Finitess?

14. Undecidable
Problem(T.M)
Halting Problem:-
Machine Can be Modified for H.P.
Can’t be Accepted by Recurive Emurable.
Hence No Solution.

15. Undecidable
Problem(T.M)
Null Words:
No Solution.
• Emptiness:
No Solution.
• Finiteness:
No Solution.
• Hence T.M is Undecidable.

16. If People Knew How I Worked Hard, They
Would Never Get Surprised ~ Anonymous

17. Books:
1. Introduction To Computer Theory By Daniel I.A
Cohen.
2. An Introduction To Formal Languages and
Automata By Peter Linz.
3. Introduction To Theory of Computation By Anil
Maheshwari, Michiel Smid.
Websites:
1. http://en.wikipedia.org/wiki/CYK_algorithm
2. http://en.wikipedia.org/wiki/Decidability
3. http://en.wikipedia.org/wiki/List_of_undecidable_pr
oblems
References

18. Thank you
for
your patience!