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To make people to be aware how to know which formal languages are decidable and why...!

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- 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!

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