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Problem 1. Let Σ = {a, b} and consider the language L1 ? Σ
? of all strings of
the form a
mu where m ≥ 0 and u has at most m many as in it. Thus, e.g., aababa
and aabba and aa are in L1, but aababaabb is not in L1.
1. Give a context-free grammar G1 = (V, Σ, R, S) that recognises the language L1.
2. Explain why your grammar is correct.
3. Explain whether or not L1 is regular.