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Consider the following statements about the context free grammar
G = {S → SS, S → ab, S → ba, S → Ε}
I. G is ambiguous
II. G produces all strings with equal number of a’s and b’s
III. G can be accepted by a deterministic PDA.

Q. Which combination below expresses all the true statements about G?
  • a)
    I only
  • b)
    I and III only
  • c)
    II and III only
  • d)
    I, II and III
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Consider the following statements about the context free grammarG = {S...
Ans.

Option (b)

G is ambiguous because, as shown in the image below there can be two decision tree for string S = ababab
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Most Upvoted Answer
Consider the following statements about the context free grammarG = {S...
Explanation:

  • Statement I: G is ambiguous


    • Since there are multiple ways to derive the same string in G, it is ambiguous.

    • For example, S can derive SS in two ways: S -> ab -> SS or S -> ba -> SS

    • Therefore, statement I is true.


  • Statement II: G produces all strings with equal number of as and bs


    • Since G only generates strings that start with either ab or ba, and each subsequent derivation adds another ab or ba pair, it is clear that G produces all strings with equal numbers of as and bs.

    • For example, S can derive ab, ba, or SS. If S derives SS, then SS can derive both abab and baba.

    • Therefore, statement II is true.


  • Statement III: G can be accepted by a deterministic PDA


    • Since G is a context-free grammar, it can be accepted by a PDA.

    • Moreover, G is unambiguous, which means that it can be accepted by a deterministic PDA.

    • Therefore, statement III is true.


  • Combination of true statements:


    • Statements I and III are true, so option B is correct.


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Consider the following statements about the context free grammarG = {S → SS, S → ab, S → ba, S → Ε}I. G is ambiguousII. G produces all strings with equal number of a’s and b’sIII. G can be accepted by a deterministic PDA.Q.Which combination below expresses all the true statements about G?a)I onlyb)I and III onlyc)II and III onlyd)I, II and IIICorrect answer is option 'B'. Can you explain this answer?
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