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Choose the correct alternatives (more than one may be correct) and write the corresponding letters only:
If G is a context free grammar and  is a string of lengthl  in L(G), how long is a derivation of ω in G, if G is in Chomsky normal form?
  • a)
    2l
  • b)
    2l+1
  • c)
    2l-1
  • d)
    l
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Choose the correct alternatives (more than one may be correct) and wri...
Chomsky Normal Form (If all of its production rules are of the form):
where A, B and C are nonterminal symbols, a is a terminal symbol (a symbol that represents a constant value), S is the start symbol, and ε is the empty string. Also, neither B nor C may be the start symbol, and the third production rule can only appear if ε is in L(G), namely, the language produced by the context-free grammar G. 
Applying productions of the first form will increase the number of nonterminals from k to k+1 since you replace one
nonterminal (-1) with two nonterminals (+2) for a net gain of +1 nonterminal. Since you start with one nonterminal, this means you need to do l-1 productions of the first form. You then need l more of the second form to convert the
nonterminals to terminals, giving a total of l+(l-1) = (2l-1) productions.
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