### Artificial IntelligenceAIMA Exercises

This exercise concerns grammars for very simple languages.
1. Write a context-free grammar for the language $a^n b^n$.
2. Write a context-free grammar for the palindrome language: the set of all strings whose second half is the reverse of the first half.
3. Write a context-sensitive grammar for the duplicate language: the set of all strings whose second half is the same as the first half.

This exercise concerns grammars for very simple languages.
1. Write a context-free grammar for the language $a^n b^n$.
2. Write a context-free grammar for the palindrome language: the set of all strings whose second half is the reverse of the first half.
3. Write a context-sensitive grammar for the duplicate language: the set of all strings whose second half is the same as the first half.

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