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ISRO | ISRO CS 2018 | Question 48

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A CFG(Context Free Grammar) is said to be in Chomsky Normal Form (CNF), if all the productions are of the form A -> BC or A -> a. Let G be a CFG in CNF. To derive a string of terminals of length x, the number of products to be used is (A) 2x – 1 (B) 2x (C) 2x + 1 (D) 2x

Answer: (A)

Explanation: A context free grammar (CFG) is said to be in Chomsky Normal Form (CNF) if all production rules satisfy the following conditions given below as :-
  1. A non-terminal symbol generate a terminal Symbol (e.g.; A->b)
  2. A non-terminal symbol generate two non-terminals symbol adjacently (e.g.; S->AB)
  3. Start symbol generating ?.(e.g.; S-> ε) and For generating string w of length ‘x’ requires ‘2x-1’ production or steps in CNF because in CNF at every step only 1 terminal can replace a variable.
Option (A) is correct.

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Last Updated : 13 May, 2020
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