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109: Theory of Computation NFA and Regular Languages omework Due hardcopy in class. You may work alone, or make a single submission for a team of 2-3 students. If you work in a team, tun in only one submission. You are expected to complete, or at least attempt, all of the following problems. Write a star on one problem; that problem is guaranteed to receive feedback and will be the basis for your grade. Each exercise is worth 9 points. 1. Prove that every finite language is regular. Hint: Give a constructive proof that explains how to start with a finite language (set of strings) A and then build an NFA that accepts any string in A. There is a "brute force" style of NFA that ends up with a total of igi-l + bol states. Sketch the NFA corresponding to A-100, 11 , 101) 2 If NFAs were restricted to have only one accept state, would they become less powerful? Let N be an arbitrary NFA. Prove that there exists an NFA N'such that N'has exactly one accept state, and L(N) L(N). Hint: One way of proving this is to give a constructive proof, where N'has one more state than does N Textbook e 2.5 Convert he LNFAto an buiveent DEA DFA 2