3. [5 pts] Consider the language of balanced square brackets. For example, both [] [] [[]]...

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3. [5 pts] Consider the language of balanced square brackets. For example, both [] [] [[]] and [[] [[]]] [[]] are in the language, while []] [[] is not. Assume the empty sequence is in the language. (a) [1] Write a context-free grammar for this language. You may use extended BNF to express the solution. (b) [1] Now assume the empty sequence is not in the language. Write a context-free grammar for the new language. You should test both of your grammars using the CFG Developer online tool at https://web.stanford. edu/class/archive/cs/cs103/cs103.1156/tools/cfg/ before submission. 3. [5 pts] Consider the language of balanced square brackets. For example, both [] [] [[]] and [[] [[]]] [[]] are in the language, while []] [[] is not. Assume the empty sequence is in the language. (a) [1] Write a context-free grammar for this language. You may use extended BNF to express the solution. (b) [1] Now assume the empty sequence is not in the language. Write a context-free grammar for the new language. You should test both of your grammars using the CFG Developer online tool at https://web.stanford. edu/class/archive/cs/cs103/cs103.1156/tools/cfg/ before submission.