Theory of computing

Anonymous
timer Asked: Apr 10th, 2017

Question Description

Construct context-free grammars for the following languages.

Question 1

CSC212 – Theory of Computing Name HW3 (Due: April 11, 2017, start-of-class) Exercise Max Nr. Pts Your Score 1 60 2 10 3 10 4 10 5 10 TOTAL 100 1. Construct context-free grammars for the following languages L1 = {an bm | n ≤ m + 4} L2 = {an bm | 2n ≤ m ≤ 3n} L3 = {an bm ck | n = m or m 6= k} 2. Eliminate all useless productions from the grammar S → a | aA | aaB | abC A → aB | λ B → Aa C → cCD D → ddd | aC 3. Eliminate all λ-productions from the grammar S → AaB | aaB | bC A → λ B → bbA | λ C → bAS | ab 4. Eliminate all unit-productions from the grammar S → abA | A | B A → B | ba | aBA B → A | aa | aA 5. Convert the following grammar into Chomsky normal form S → aABb A → aBa | a B → cAa | ba

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