Consider the following languages over - - a-bL1-ww-w- a-b-L2 - complement of L1L3 - L1- L2Which of the above languages is Recursively enumerable but not context free language-

Option (a) L_1 is REL but not CFL L_2 is CFL L_3 = (a+b)^* L_1∪L̅_̅1̅= L_1 ∪ L_2 is CFL ...

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Consider the ...

Question

Consider the following languages over $\sum = {a, b} L_{1} = {w w | w \in {a, b} *} L_{2} = complement of L_{1} L_{3} = L_{1} \cup L_{2}$
Which of the above languages is Recursively enumerable but not context free language?

L_{1} o n l y

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B o t h L_{1} a n d L_{2}

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L_{2} o n l y

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L_{1} a n d L_{1}

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Solution

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L_{1} a n d L_{2}

L_{1}

L_{2}

_{1}

L_{1}

_{2}

L_{2}

_{1}

_{1} \cup L_{2}

L_{1}

L_{2}

L_{1} : {w w | w ϵ {a}^{*}}

L_{2} : {w w | w ϵ {a b}^{*}}

L_{1} : R e g u l a r, L_{2} : C o n t e x t - f r e e, L_{3} : R e c u r s i v e, L_{4} : R e c u r s i v e l y e n u m e r a b l e .

_{3} \cup L_{4}

_{2} \cup L_{3}

_{1} \cap L_{2}

L_{1} \cup_{2}

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