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Question Paper Code:: Reg. No.

The document is a question paper for a theory of computation exam. It contains 15 questions split into 3 parts - short answer questions in Part A, longer answer questions in Part B, and longer theoretical proofs or explanations of computational concepts in Part C. The questions cover topics like Turing machines, recursively enumerable languages, complexity classes such as P, NP, L, NL and their relationships, as well as computational problems like the halting problem and problems relating to cryptography.

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Srinivas Rangarajan
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87 views2 pages

Question Paper Code:: Reg. No.

The document is a question paper for a theory of computation exam. It contains 15 questions split into 3 parts - short answer questions in Part A, longer answer questions in Part B, and longer theoretical proofs or explanations of computational concepts in Part C. The questions cover topics like Turing machines, recursively enumerable languages, complexity classes such as P, NP, L, NL and their relationships, as well as computational problems like the halting problem and problems relating to cryptography.

Uploaded by

Srinivas Rangarajan
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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*X65570*

Reg. No. :

Question Paper Code : X65570


B.E./B.Tech. DEGREE Examinations, november/december 2020
Sixth Semester
Computer Science and Engineering
080230026 – theory of computation
(Regulations 2008)

Time : Three Hours Maximum : 100 Marks

Answer all questions


Part – A (10×2=20 Marks)

1. Define Turing Machine.

2. Relate recursive and recursively enumerable language.

3. What is a multitape Turing machine ?

4. Prove that the function f (n) = n – 1 is computable.

5. What is meant by a verifier for a language ?

6. When is a language said to be NP-complete ?

7. What is class L and NL ?

8. What do you mean by Oracle Turing machine ?

9. Define BPP.

10. What is trapdoor function ?

Part – B (5×16=80 Marks)

11. a) i) Construct a Turing machine for the set of all strings of balanced
parenthesis. (8)
ii) Show that ‘every language accepted by a multitape Turing machine is
recursively enumerable’. (8)
(OR)
X65570 *X65570*

b) i) Let f be the function f (n) = n – 1, when n > 0 and f (0) = 0 . Show that f is
decidable. (8)
ii) Prove that Halting problem is undecidable. (8)

12. a) i) Prove that union and intersection of two recursive languages are also
recursive. (8)
ii) Prove that there exists an recursively enumerable language whose complement
is not recursively enumerable. (8)
(OR)
b) State and Prove Rice’s theorem. (16)

13. a) Prove that 3SAT is polynomial time reducible to CLIQUE.


(OR)
b) Prove that SUBSET-SUM is NP-complete.

14. a) i) Let f : N->R be a function with f(n) ≥ n then prove that


NSPACE(f(n))⊆ SPACE (f 2(n)). (10)
ii) Discuss briefly about Generalized Geography game. (6)
(OR)
b) i) Prove that NL = coNL. (8)
ii) Write short notes on circuit complexity. (8)
15. a) i) Define and prove Fermat’s theorem. (8)
ii) Write and prove the approximation algorithm for vertex cover problem. (8)
(OR)
b) i) Define and prove that IP PSPACE. (8)
ii) Explain the public key cryptosystems. (8)

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