How can I achieve this. Write a grammar for the language consisting of strings built only of the letters a and b. The strings may have any number of these letters, but the letter combinations bab must be in each string somewhere, and each string must start with a bb. For example, the strings bbababbbaa, bbbaaaababaa, and bbbab are in the language, while a, aabb, baaa, and bbba are not.

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    $\begingroup$ Your language is regular. You can design an NFA for your language, and then convert it to a context-free grammar. $\endgroup$ – Yuval Filmus May 16 '19 at 20:05
  1. The string much start with $ bb $ .
  2. There should at least one occurrence of the sub-string $ bab $

Hence, the structure of the regular expression must be something like this: $$ bb[some \: string]bab[some \: string] $$

and, we can define $ [some \: string] $ something like this:

$$ (a + b)^* $$

which means, there can be any number (including 0) of either a's or b's. Therefore, the final regex for the word is, $$ bb(a+b)^*bab(a+b)^* $$

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    $\begingroup$ Doesn't match $bbab$. $\endgroup$ – rici May 16 '19 at 20:32
  • $\begingroup$ Thank you! I figured it out now. $\endgroup$ – Lizzy May 16 '19 at 20:46

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