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CPSC 439: Theory of Computation Homework 1: DFAs and NFAs students. If you work in a team, tun in only one submission. Due hardcopy in class. You may work alone, or make a single submission for a team of 2-3 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 Exercise 1 (3 points): Sketch a DFA for each of the following languages. In each case the alphabet is 2 10,1) a) (w:100 is a substring of w) b) (w:100 is not a substring of w! c) (w: w contains at least two Os and at least one 1) Show your work. 1 point 1 point] I1 point Exercise 2 (3 points): Sketch a NFA with the specified number of states for each of the following languages. In each case the alphabet is 2-(0,1). [1 point (1 point] a) (w: w ends in 01) with three states. b) (w: w contains the substring 0110 with five states. c) (w: w contains an odd number of ones or exactly two Os Show your work [1 point Exercise 3 (3 points): Let A and B be two regular languages over the same alphabet. Prove that the difference of A and B, i.e. the language A \ B {w: wEA and WEB) is a regular language. Show your work. Hint: Give a constructive proof similar to the proof of Theorem 2.3.1 Tupie