Code No. 2209 / O

FACULTY OF INFORMATICS B.E. 3/4 (IT) I-Semester (Old) Examination, November / December 2012 Subject: Theory of Automata Time : 3 Hours

Max. Marks: 75

Note: Answer all questions of Part - A and answer any five questions from Part-B. PART – A (25 Marks) 1. Over alphabet ={a, b} and write a regular expression with even number of 'a' s followed by odd number of 'b's and draw FA? 2. Give any two applications of FA. 3. Show that regular languages are closed under union, concatenation and kleen star. 4. Obtain grammar to generate string consisting of any number of a's and b's with atleast one 'a'. 5. What is homomorphism? 6. Eliminate '' productions S  AB ; A  aAA /  ; B  b BB /  7. What is the advantage of stack in PDA? 8. Define Multitape Turing machine. 9. State Halting problem. 10. What is meant by undecidability?

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PART – B (5x10=50 Marks) 11.(a) Convert NFA in DFA

(b) Obtain a regular expression for the language L={anbm / m 1, n  1, nm  3}

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12.(a) State and prove pumming lemma for regular language. (b) Show that the following grammar is ambiguous SaSbS SbSaS S  13. Obtain a PDA to accept the language L(M) = {w/w  (a+b)* and na(w)=nb(w)} by a final state i.e. no. of. a's in string w should be equal to no. of. b's in w.

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14. Obtain a Truing Machine to accept palindrome consisting of a's and b's of any length.

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15.(a) When do you say that a problem is undecidable ? Explain. (b) Explain with example P and NP problem.

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16.(a) What is post correspondence problem? (b) Give an instance of PCP, show that this instance has solution or not (c) Define CNF and GNF List A List B i wi Xi 1 011 101 2 11 011 3 1101 110

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17. Write short notes on: (a) Church's hypothesis (b) Recursive and recursively enumerable sets (c) Rice theorem *****

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