DECIDABILITYBy:

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

ContentsIntroduction

Advantages

Decidability in Automata

Types:

◦ Decidable

◦ Semi-Decidable

◦ Undecidable

Decidable Problems

◦ For C.F.L

◦ For F.A

Undecidable Problems

◦ For T.M

References

Introduction

An Effective solution to a problem that has

“Yes” or “No” answer.

Having Decision procedure is known as

Decidable.

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:

Decidable

Semi-decidable

Un-decidable

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

practically.

Undecidable

Existing no effective algorithm

Solutions can not be determined

Decidable

Problems(C.F.L)

Emptiness?

Finiteness?

Membership?

Solution:-

Emptiness:

Convert CFG into CNF.

Finiteness:

Apply Pumping Lemma.

Membership:

Apply CYK algorithm on CNF form.

Hence CFL is Decidable.

Decidable

Problems(C.F.L)

Decidable Problems(F.A)

Is the same Language accepted by two

different F.As?

Is the same Language defined by two different

R.Es?

Solution:-

Convert both F.A’s into Regular Expression.

Get a minimum word Accepted by both.

Hence FA is Decidable.

Decidable Problems(F.A)

Undecidable

Problem(T.M)

The Halting Problem?

Null Words?

Emptiness?

Finitess?

Halting Problem:-

Machine Can be Modified for H.P.

Can’t be Accepted by Recurive Emurable.

Hence No Solution.

Undecidable

Problem(T.M)

Null Words:No Solution.

• Emptiness:No Solution.

• Finiteness:No Solution.

• Hence T.M is Undecidable.

Undecidable

Problem(T.M)

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 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_problems

References

Thank you

for

your patience!