1. Consider the NFA defined by the state diagram below. Follow the algorithm seen in class and in our textbook to construct an equivalent DFA. Please only include the states reachable (in one or more transitions) from the start state. (Your solution can be either the table or the state diagram, or both if you wish.) a ε, b b a a 92 91 8 93 b a, b

- a) Answer these Theoretical Questions: 1. Explain the rule of thumb for the Big O. Provide at least one example of applying each rule. 2. What is the Big O of each of the following functions? a) (n + 1)³/n b) (n³ + logзn) ³/n c) n + 100n³ + n d) 3n+ 100n3 + 3n * e) n 3n+ n * 33n 3. Describe an algorithm for finding the occurrence of the max element in an array. Analyze the complexity of the algorithm. 4. What is Divide-and-Conquer? What is the difference between Divide-and-Conquer and Dynamic Programming? What are the benefits of using one over another if any? 5. Is it possible to design an algorithm for finding the max element in a list using Divide-and-Conquer? What is the complexity of this algorithm? Hint: In this approach, the initial array is divided into two halves... b) Programming assignment: Implement initiative / naïve method to find a max element in an array. Implement the method that uses the Divide-and-Conquer approach to find the max element in an array. Test both…

9. Given the following Boolean Function: F(P, Q, R) = PQ+QR+PR F(P,Q,R) (i) Derive the canonical SOP (sum of minterms) for F. (ii) Derive the canonical POS (product of maxterms) for F. (iii) Draw the truth table, clearly marking which rows are minterms of F and which rows correspond to maxterms of F. 10) For n Boolean variables, how many distinct Boolean functions exist? Give the answer as a function of n and briefly justify it.