$1.$ Construct a npda that accepts the language generated by the grammar

$$ S $$ aSb $|$ bSa $|$a $|$ b $|$ab$.$

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Answer:

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For Questions $6,7$ and $8,$ let nx$($w$)$ denote the number of x$$s in a string w$.$

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$2.$ Show that the language L $=\{$w $\{$a$,$ b$\}*$ : na$($w$)<$ nb$($w$)\}$ is a context$-$free language by constructing a npda to accept it$.$

Answer: