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Theory of Computation Course Code: 10B11CI513 ASSIGNMENT – II Last Date: 30-11-2018 1. a) Discuss ambiguity, left recursion and factoring in context free grammars. Explain how to eliminate each one. b) Discuss closure and decision properties of context free languages. 2. What is GNF? Explain in detail. Convert the following grammar to GNF: a) A 1 A 1 A 3 b) A 2 A 3 A 1 |b c) A 3 A 1 A 2 |a. 3. a) Reduce the grammar S aAa, A SB|bcc|DaA, C abb|DD, E ac, D aDA. b) What is left recursion? How to eliminate it? 4. a) Convert the given grammar to GNF: i) A 1 A 1 A 3 ii) A 2 A 3 A 1 |b iii) A 3 A 1 A 2 |a. b) Explain the concept of ambiguity in context free grammars. How to eliminate it? 5. Convert the following grammar into Chomsky normal form: S aA/a /B/c, A a B/  B aA, C c C D, D abd. 6. a) What are useless variable in a CFG? How do you find out useless variable in a given CFG? Explain with an example.

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