1. Construct a dfa that accepts the language generated by the grammar S→ abA, A→ baB, B→ aA|bb. 2. Find a regular grammar that generates the language L (aa* (ab+ a)*). 3. Construct a left-linear grammar for the language in Exercise 1. 4. Construct right- and left-linear grammars for the language L = {a"b™ : n2 2, m2 3}. 5. Adapt the construction in Theorem 3.4 to find a left-linear grammar for the language accepted by the nfa below. 6. Construct a right-linear grammar for the language L ((aab*ab)*). 7. Find a regular grammar that generates the language on E = {a, b} consisting of all strings with no more than three a's.

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Modular arithmetic is a system of arithmetic for integers, whose values reset to zero and begin to increase again, after reaching a certain predefined value, called the modulus (modulo). Modular arithmetic is widely used in computer science and cryptography.