Consider the languages: L1 = {anbncm | n, m > 0} L2 = {anbmcm | n, m > 0}…

2005

Consider the languages:

L1 = {anbncm | n, m > 0}

L2 = {anbmcm | n, m > 0}

Which one of the following statements is FALSE?

  1. A.

    L1 ∩ L2 is a context-free language

  2. B.

    L1 U L2 is a context-free language

  3. C.

    L1 and L2 are context-free language

  4. D.

    L1 ∩ L2 is a context sensitive language

Attempted by 19 students.

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Correct answer: A

L1 = {anbncm | n, m > 0} and L2 = {anbmcm | n, m > 0} are both context-free languages. Their intersection L1 ∩ L2 requires strings to have equal numbers of a, b, and c in the form anbncn. This language is not context-free because it requires two comparisons (a=b and b=c), which cannot be handled by a single stack. Therefore, L1 ∩ L2 is not context-free and must be at least context-sensitive.

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