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DECIDABILITY 
By: 
M.Daniyal Ashfaq (2013-CS-51) 
Shahrukh Mahesar (2013-CS-32) 
M.Waleed Aslam (2013-CS-14) 
Sagar Kumar ...
Contents 
Introduction 
Advantages 
Decidability in Automata 
Types: 
◦ Decidable 
◦ Semi-Decidable 
◦ Undecidable 
Decida...
Introduction 
An Effective solution to a problem that has 
“Yes” or “No” answer. 
Having Decision procedure is known as 
D...
Advantages 
Determined Goal. 
Strong Procedure. 
More Accurate. 
Time Saving.
Decidability in Automata 
An algorithm, determining the validity of a 
given input. 
Divided into three parts: 
 Decidabl...
Decidable 
Existance of an effecive algorithm 
Ability to determine whether an input is 
acceptable or not.
Semidecidable 
Existance of an Algorithm, having effectiveness 
in theory 
Sometimes fail to determine exact answer 
pract...
Undecidable 
Existing no effective algorithm 
Solutions can not be determined
Decidable 
Problems(C.F.L) 
Emptiness? 
Finiteness? 
Membership?
Decidable 
Problems(C.F.L) 
Solution:- 
Emptiness: 
Convert CFG into CNF. 
 Finiteness: 
Apply Pumping Lemma. 
Membersh...
Decidable Problems(F.A) 
Is the same Language accepted by two 
different F.As? 
Is the same Language defined by two differ...
Decidable Problems(F.A) 
Solution:- 
 Convert both F.A’s into Regular Expression. 
 Get a minimum word Accepted by both....
Undecidable 
Problem(T.M) 
The Halting Problem? 
Null Words? 
Emptiness? 
Finitess?
Undecidable 
Problem(T.M) 
Halting Problem:- 
Machine Can be Modified for H.P. 
Can’t be Accepted by Recurive Emurable. ...
Undecidable 
Problem(T.M) 
Null Words: 
No Solution. 
• Emptiness: 
No Solution. 
• Finiteness: 
No Solution. 
• Hence ...
If People Knew How I Worked Hard, They 
Would Never Get Surprised ~ Anonymous
Books: 
1. Introduction To Computer Theory By Daniel I.A 
Cohen. 
2. An Introduction To Formal Languages and 
Automata By ...
Thank you 
for 
your patience!
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Deciability (automata presentation)

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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...!

Published in: Software
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Deciability (automata presentation)

  1. 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. 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. 3. Introduction An Effective solution to a problem that has “Yes” or “No” answer. Having Decision procedure is known as Decidable.
  4. 4. Advantages Determined Goal. Strong Procedure. More Accurate. Time Saving.
  5. 5. Decidability in Automata An algorithm, determining the validity of a given input. Divided into three parts:  Decidable  Semi-decidable  Un-decidable
  6. 6. Decidable Existance of an effecive algorithm Ability to determine whether an input is acceptable or not.
  7. 7. Semidecidable Existance of an Algorithm, having effectiveness in theory Sometimes fail to determine exact answer practically.
  8. 8. Undecidable Existing no effective algorithm Solutions can not be determined
  9. 9. Decidable Problems(C.F.L) Emptiness? Finiteness? Membership?
  10. 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. 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. 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. 13. Undecidable Problem(T.M) The Halting Problem? Null Words? Emptiness? Finitess?
  14. 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. 15. Undecidable Problem(T.M) Null Words: No Solution. • Emptiness: No Solution. • Finiteness: No Solution. • Hence T.M is Undecidable.
  16. 16. If People Knew How I Worked Hard, They Would Never Get Surprised ~ Anonymous
  17. 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. 18. Thank you for your patience!

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