Consider the following languages. L1 = {ai bj ck | i = j, k ≥ 1} L1 = {ai bj |…

2008

Consider the following languages.

L1 = {ai bj ck | i = j, k ≥ 1}

L1 = {ai bj | j = 2i, i ≥ 0}

Which of the following is true?

  1. A.

    L1 is not a CFL but L2 is

  2. B.

    L1 ∩ L2 = ∅ and L1 is non-regular

  3. C.

    L1 ∪ L2 is not a CFL but L2 is

  4. D.

    There is a 4-state PDA that accepts L1, but there is no DPDA that accepts L2

Attempted by 19 students.

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Correct answer: B

The correct answer is that L1 = {a^i b^j c^k | i = j, k ≥ 1} is a context-free language (CFL), while L2 = {a^i b^j | j = 2i, i ≥ 0} is also a CFL. Both languages require counting and matching symbols, which can be done with a pushdown automaton (PDA). Therefore, both are context-free languages.

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