Final answer:
The CFG L2 is for palindromic strings over the binary alphabet with lengths that are multiples of 7. A palindrome reads the same forwards and backwards. The production rules of the CFG create symmetrical strings of specified lengths.
Step-by-step explanation:
The given CFG L2 represents the language of palindromic strings over the alphabet {0, 1} where the length of the string is a multiple of 7. In formal languages and automata theory, a palindrome is a string that reads the same forward and backward, such as '010' or '11011'. To satisfy the condition that the length of the word (|w|) is a multiple of 7, any string generated by this CFG must have lengths like 7, 14, 21, etc.
The CFG for such a language can be represented in a way where production rules systematically expand to create strings that are symmetrical (palindromic) while ensuring that the length of the generated strings adheres to the specified multiple of 7.
As an example, to construct a palindromic string of length 7, we can use the following productions: S → aSa | bSb | ε ; where S is the start variable, a and b represent '0' and '1' respectively, and ε is the empty string used here to denote the middle of the palindrome. Generating a string of length 14 would involve additional layers of recursion in the production rules, iterating until the string length requirement is met.