Question: Did I do this problem correctly? Question: Construct context-free grammars that generate the following languages (give your answers as a set of rules): {a k

Did I do this problem correctly?

Question:

Construct context-free grammars that generate the following languages (give your answers as a set of rules):

  1. {akw|w{a,b},|w|=k,k0}

Answer:

S | A

A | aAB

B a | b

Possible strings to test on:

k = 1

-> |w| = 1 -> aa | ab

SAaAB aB aBaa | ab

k = 2

-> |w| = 2 -> aaaa | aabb | aaab | aaba

SAaAB aaABBaaBBaaBBaaaa aabb aaab | aaba

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