Question

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 bb must be in each string somewhere, and each string must end with a ba.

Answer 1

Answer:

Grammer:

S->ABS/bba

A->aA/ab

B->bB/ba

Output:

1. abbabba
2. aabbbabba
3. bba

Explanation:

The above grammar satisfies the question because the question says that there is a combination of string made by 'a' and 'b' which ends with 'ba' and there is somewhere 'bb' in the string. Prove of the above grammar is as follows--

• Take the 'S' and replace it with 'ABS'. Then 'A' will replace with 'ab' and 'B' will replace with 'ba' and 'S' will replace with 'bba' then the string will "abbabba", which is the first output.
• Take the 'S' and replace it with 'ABS'. Then A will replace with 'aA' and 'B' will replace with 'bB' and 'S' will replace with 'bba' then further 'A' will replace with 'ab' and 'B' will with 'ba' and then the string will "aabbbabba", which is the second output.
• Take the 'S' and replace it with "bba" and the string will "bba".

So the question says that there is a string ending with 'ab' and there exits 'bb' in anywhere. so all the output define above satisfies the condition and all other output also satisfies the condition.