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Consider the following grammar G:
S → X|a|YXZ
X → Y∣b
Y → S∣c
Z → d
After removing the left recursion how many Production Rules exist in the grammar.
(In G there are 8 Production Rules)
  • a)
    13
  • b)
    12
  • c)
    11
  • d)
    14
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Consider the following grammar G:S → X|a|YXZX → YbY → S...
Given:
S → X|a|YXZ
X → Y∣b
Y → S∣c
Z → d
Substitute to X production in S.
S → Y|b|a|YYZ|YbZ
Y → S∣c
Z → d
Substitute to Y production in S.
S → c|b|a|SZ|ccZ|ScZ|cSZ|SbZ|cbZ
Z → d
Left recursion of above productions is,
S → SZ ⇒ S → pX′,X′ → ZX′/ε
S → ScZ ⇒ S → pY′,Y′ → cZY′/ε
S → SbZ ⇒ S → pZ′,Y′ → bZZ′/ε
Total productions are:
S → pY′,Y′→cZY′/ε
S → pX,X→ZX′/ε
S → pZ′,Y′→bZZ′/ε
S → c|b|a|ccZ|cSZ|cbZ
Z → d
So, the total productions are 13.
Hence, the correct answer is (A)
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