CS MidTerm Exam 4/1/2004 Name: KEY. Page Max Score Total 139

Transcription

1 CS MidTerm Exam 4/1/2004 Name: KEY Page Max Score Total 139 %

2 INTRODUCTION, AI HISTORY AND AGENTS 1. [4 pts. ea.] Briefly describe the following important AI programs. Give the last names of their authors, and briefly state why they were important a. General Problem Solver Herbert Simon and Allen Newell The first reasonin system that accepted and used domain specific information to solve a variety of problems. It was an improvement over the Logic Theorist program that could only prove theorems b. MYCIN Buchanan, Shortliff, Fiegenbaum The first widely successful medical diagnosis systems used to diagnose diseases given information from blood tests and other patient data. Performed as well as undergraduate medical students 2. [3 pts. ea.] Briefly describe or define the following: a. Artificial Intelligence The study of programs that exhibit intelligent behavior b. Heuristic A rule of thumb that often is correct, but is not guaranteed to be correct 3. [4 pts.] Name two features that distinguish AI programs from non-ai programs? Sophisticated problem solving, such as search, planning, inference, etc. Uses knowledge Can learn 1

3 UNINFORMED SEARCH 4. [4 pts.] The figure below shows a tree-shaped search space. The search starts with the node labeled 0 on the queue. The only node containing a goal state is the node labeled B2a. List, in order (nodes are opened left-to-right), the nodes that will be examined by iterative deepening depth-first search. 0, 0, A, B, C, 0, A, A1, A2, B, B1, B2, C, C1, C2, 0, A, A1, A1a, A2, A2a, B, B1, B2, B2A 0 A B C A1 A2 B1 B2 C1 C2 A1a A2a B2a C1a C1b INFORMED SEARCH 5. [3 pts.] Briefly describe or define admissible heuristic A heuristic used in A* search for estimating the cost to reach the goal node from the current node that never overestimates the cost 6. [4 pts.] How does A* search improve upon best-first search? A* uses the actual cost from the start node to the current node and only estimates the remaining distance to the goal node, while best-first search estimates the entire cost of a path to the goal node from the start node and going through the current node. In other words, A* factors in the known costs that it can, allowing A* to give a better estimate. A* also imposes a constraint that the heuristic never overestimates the actual cost of reaching the goal node from the current node 2

4 7. [30 pts.] Below is a map of the cities around Bucharest, and a chart of straightline distances to Bucharest. Show the search tree generated by A* searching for a path from Oradea to Bucharest using the straight-line heuristic for h(n). Show f(n), g(n), and h(n) for each node. Number your nodes by the order in which they are examined. Oradea Zerind Arad Timisoara 111 Lugoj 70 Mehadia 75 Dibreta Rimnicu 146 Craiova 97 Fagaras 138 Pitesti Straight-line distance to Bucharest Arad 366 Fagaras 178 Mehadia Bucharest 0 Giurgiu 77 Neamt 234 Timisoara 329 Craiova 160 Hirsova 151 Oradea 380 Urziceni 80 Dobreta 242 Iasi 226 Pitesti 98 Vaslui 199 Eforie 161 Lugoj 244 Rimnicu 193 Zerind Giurgiu 211 Neamt 87 Urziceni Bucharest Iasi 92 Vaslui Hirsova 86 Eforie Zerind 445= Oradea 682 = Oradea 380 = = Arad 657 = = Rimnicu 537 = Rimnicu 424 = Pitesti 426 = Craiova 626 = City F(n) = g(n) + h(n) 5 Fagaras 428 = Craiova 537 = Bucharest 429 = = Bucharest 761 =

5 LOCAL SEARCH 8. [3 pts.] Briefly describe how crossover works in genetic algorithms Crossover randomly swaps sections of the bits encoding two parents 9. [3 pts. ea.] Give the name (and very briefly state why) of the algorithm that results from each of the following special cases: a. Simulated annealing with T = 0 at all times. First-choice hill climbing: chooses the first randomly chosen successor that improves over the current state. b. Genetic algorithm with population size N = 1. Stochastic hill climbing: probabilistically (1/fitness) choose 1 successor node GAME PLAYING SEARCH 10. [3 pts. ea.] Briefly describe or define the following: a. Zero-sum game A two-player game where one player must win and the other player must lose, or there is a draw, in this case, if the reward for winning (e.g., +1) is equal in magnitude to the penalty for losing (e.g., -1), then the utilities (penalties and rewards) of the players sum to zero. b. Horizon effect When using minimax game playing analysis, one can only examine the search tree so far, so one must use a cutoff for the search depth. There is always the chance that just beyond that cutoff i.e., the horizon) are a series of moves that are disastrous, but cannot be detected. 4

6 11. Consider the game search tree in the figure below. Assume the first player is the MAX player and the values at the leaves of the tree reflect his/her utility. MAX A 4 MIN B C 4 2 MAX D E F G MIN H I J K L M N O a. [20 pts.] Compute the minimax values for each node in the tree. b. [2 pts.] What move should MAX choose? Why? MAX should choose B, because B will maximize MAX s outcome, assuming that MIN and MAX are optimal players c. [8 pts.] Mark or list all nodes that are cut off from the tree and are never explored by the alpha-beta procedure. Assume that successors are expanded left-to-right. d. [3 pts.] In general, what order should nodes be examined in order to obtain the greatest benefit from alpha-beta pruning? For MAX, nodes should be examined in descending order For MIN, nodes should be examined in ascending order PROPOSITIONAL LOGIC AND INFERENCE 12. [3 pts. ea.] Briefly describe or define the following: a. Inference The process of deriving new facts from existing ones b. Soundness An inference method only makes correct inferences from a knowledge base c. Completeness An inference method makes all possible inferences from a knowledge base d. Entails A knowledge base entails a sentence if the sentence is derivable from the knowledge base. Also: a KB entails a sentence iff in all models where KB is true, so is the sentence 5

7 13. [20 pts.] Use a truth table to show by enumeration that KB S. KB: P & Q & ( P R) & ( Q R S) P Q R S ( P R) ( Q R S) KB T T T T T T T F T T T T T F T F T T T T F F F T T T T F T T F T F T F F T F T T T F T F F T F T F F F F T T T F T T T F T F F F T T F T F F T F T F T T F F F T F T T F T T F F F T F F T F F T T F T F F F F T F F F F F T T F Since every time the KB is true (shown in bold), S is true (also shown in bold), then KB S. 6