Computer Engineering (Semester 5)
Total marks: 80
Total time: 3 Hours
INSTRUCTIONS
(1) Question 1 is compulsory.
(2) Attempt any three from the remaining questions.
(3) Draw neat diagrams wherever necessary.
1.a.
Explain Chomsky Hierarchy.
(5 marks)
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1.b.
Difference between PDA and NPDA.
(5 marks)
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1.c.
Define regular expression and give regular expression for
i) Set of all strings over {0,1} that end with 1 and has no substring 00
(5 marks)
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1.d.
Explain Halting Problem
(5 marks)
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2.a.
Define the finite state machine to determine the ternary number (base 3) is divisible 5.
(10 marks)
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2.b.
Give and explain formal definition of Pumping Lemma for Regular Language and prove that the following language is not regular
(10 marks)
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3.a.
Construct PDA accepting the language
(10 marks)
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3.b.
Consider the following grammar
for the string 'ibtaeibta' find the following :
(i) Leftmost Derivation
(ii)Rightmost derivation
(iii)Parse tree
(iv)Check if above grammar is ambiguous.
(10 marks)
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4.a.
Construct TM to check wellformness of parenthesis.
(10 marks)
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4.b.
Convert following CFG and CNF
(10 marks)
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5.a.
Convert (0+1)(10)*(0+1) into NFA with $\epsilon$-moves and obtain DFA.
(10 marks)
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5.b.
Construct Moore and Mealy machine to convert each occurence of 100 by 101.
(10 marks)
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6
Write short note on any four -
(a)Closure properties of Context Free Language
(b)Applications of Regular expression and Finite automata.
(c)Rice's Theorem
(d)Moore and Mealy Machine.
(e)Universal Turing Machine
(20 marks)
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