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A

Section A: Long Answer Questions

Attempt any TWO questions.

3 questions·10 marks each
1long10 marks

Define a Turing Machine formally. Design a Turing Machine that accepts the language L = { a^n b^n c^n | n >= 1 } and explain its working with a transition diagram.

turing-machinerecursively-enumerable
2long10 marks

Explain the relationship between regular expressions and finite automata. Show that for every regular expression there is an epsilon-NFA accepting the same language, and convert (a+b)*ab into an equivalent finite automaton.

regular-expressionepsilon-nfa
3long10 marks

State the Halting Problem of a Turing Machine. Prove that the Halting Problem is undecidable. Differentiate between decidable and undecidable problems with examples.

halting-problemdecidability
B

Section B: Short Answer Questions

Attempt any EIGHT questions.

9 questions·5 marks each
4short5 marks

Explain the conversion of a CFG into Greibach Normal Form (GNF).

greibach-normal-formcfg
5short5 marks

Define instantaneous description (ID) of a PDA and explain acceptance by final state and by empty stack.

pda
6short5 marks

Explain the working of a multi-tape Turing Machine.

turing-machine
7short5 marks

What is a Universal Turing Machine? Explain its significance.

turing-machineuniversal-tm
8short5 marks

Differentiate between recursive and recursively enumerable languages.

recursiverecursively-enumerable
9short5 marks

Define Mealy and Moore machines and differentiate between them.

mealy-moore
10short5 marks

Explain the closure properties of regular languages.

closure-propertiesregular-languages
11short5 marks

What is the membership problem? Explain the CYK algorithm in brief.

cykdecidability
12short5 marks

Construct an NFA for the regular expression (0+1)*1.

nfaregular-expression