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PART - 8

(5 x 12 = 60 MARKS)

ANSWER ANY FIVE QUESTIONS

1. a) Prove the following by ciple of induction.prin. 61.1! + 2.2! +3.3! + ........... + n.n! = (n+1)!-1, n> 1.

)Show that L = {On 10nI n1} is not regular 6

2.a) Discuss about the Chomsky hierarchy of languages. 4

)Construct a NFA that accept the set of all strings {a, b} ending with "aba" as 8

substring and construct DFA.

23 a) Find a deviation tree of a * b + a * b given that a * b + a * b is in L(G), where 4

G is given by S S + S, S S * S, S a / b

b) Find the CNF for the following grammar 8

" S AS I as, A aab IE, S bba

24

.

a) Show that the language L = {an bn

cn

dnI nO} is not CFL 6

b) Discuss the models of Turing machines. 6

5 Design PDA for the language L = {a3n

bnI nO} and simulate its action on

the input string aaaaaabb.

6. a) Show that the language L and its complement L' are both recursively 6

enumerable then L is recursive.

b) Explain the halting problem Is it decidable or undecidable problem 6

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27. Write a short notes on the following

a) Universal Turing machine

b) Post Correspondence Problem6

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28. a) Prove that a problem p2 cannot be solved in polynomial time can be proved 6by the reduction of a problem p1, which is under class p1 to p2.

b)Write a note on NP - Completeness. 6

*****THE END*****

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