Artificial Intelligence - Special Cases of Local Search Algorithms 1. Give the name of the algorithm that results from each of the following special cases of local beam search:      (a) Local beam search with k = 1.      (b) Local beam search with one initial state and no limit on the number of states retained

Problem 3. (a) Describe an algorithm that takes as input an integer n and computes n! (b) Find the running time function T(n) of this algorithm.

Problem 7: Design a finite state machine that accepts all finite binary strings except those with some occurrence of "000" or "111" in them. (Optional challenge): Modify the finite state machine so it also accepts strings with both "000" and "111" in them.

1. (a)The objective is to shuffle a given array of n different elements. You would like to compare various shuffling algorithms and select the best of them. What does it mean: “the best shuffling algorithm”? What is a requirement for the perfect shuffling algorithm? (b) Is the Fisher-Yates Shuffle the perfect shuffling algorithm? Present a formal mathematical proof that this algorithm meets (or does not meet) the requirement given in (a). (c)  Evaluate empirically performance of the Fisher-Yates Shuffle for selected numerical values of n. Propose your evaluation criteria and explain your evaluation methodology. Report your observations and conclusions.