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Section 3 CS182 Intelligent Machines: Reasoning, Actions and Plans

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Tic-Tac-Toe

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A Variation of Tic-Tac-Toe Diagonal row (5 point!), vertical row (3 point!) and horizontal row (1 point!) Suppose you play and it’s your turn now:

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Game Tree

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Utilities +1 -3 -5 +1+3 -3 +1 +3+1 -5 +1 -3

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Solve the Game 1 -3 1 1 3-331-3 1-5 1331 1

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Alpha-Beta Pruning

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Alpha-Beta Pruning By Hand! 1 -3-3-3 1 -5 13311 1-3 3 1 -511 1

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Evaluation Function Sometimes we really can’t make it to the terminal nodes… Cut-off tests and evaluation functions – How likely is this node to lead to a win? Evaluation function for Tic-tac-toe? -How many rows/columns your crosses/circles spread? -Among all diagonal/vertical/horizontal rows, how many are still reachable? -Winning patterns?

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Constraint Satisfaction Problem: Can we graduate?

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CSP for course requirements (1) Alby-Bach University (ABU) wants to start a new degree program: B.S in Judgment Day Prevention (JDP). Suppose the degree program is associated with the following courses: 15-211 Fundamental Data Structures and Algorithms 15-212 Principles of Programming 15-381 Artificial Intelligence: Representation and Problem- Solving 15-681 Machine Learning 80-310 Logic and Computation 21-484 Graph Theory 70-122 Accounting 70-311 Organizational Behavior 19-601 Information Warfare

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CSP for course requirements (2) In order to graduate from the degree program, one must complete the following four requirements: Algorithms Requirement: (15-211 AND 15-212) OR (15- 211 AND 15-381) OR (15-681 AND 21-484) Machine Learning Requirement: 15-381 OR 15-681 OR 80-310 Communications Requirement: 21-484 OR 70-311 OR 70- 122 Information Warfare Requirement: 15-381 OR 19-601

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CSP for course requirements (3) In addition, the department imposes the following restrictions: Information Aggressiveness Restriction: So that they can’t make their programs TOO smart, students can take only one class from the set 15-381, 15-681, and 19-601. Basic Arithmetic Restriction: Students can’t take both 15-211 and 70-122. Organization Restriction: Students can’t take both 21-484 and 70-311. Finally, courses cannot be used to count towards multiple graduation requirements - so if you use 15-381 to fulfill part of the Algorithms requirement it can’t count towards either the Machine Learning Requirement or the Information Warfare Requirement.

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Model the problem as CSP (1) What are the variables? o AR_1 o AR_2 o MLR o CR o IWR

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Model the problem as CSP (2) What are the domains? o AR_1: 15-211, 15-212, 15-381, 15-681, 21-484 o AR_2: 15-211, 15-212, 15-381, 15-681, 21-484 o MLR: 15-381, 15-681, 80-310 o CR: 21-484, 70-122, 70-311 o IWR: 15-381, 19-601

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Model the problem as CSP (3) What are the constraints? o IAR: 1 of 15-381, 15-681, and 19-601 can be assigned to the 5 variables. o BAR: 1 of 15-211 and 70-122 can be assigned to the 5 variables o OR: 1 of 21-484 and 70-311 can be assigned to the 5 variables o No double counting: if a variable is assigned to one variable it can’t be assigned to another variable o Hidden constraint between AR_1 and AR_2

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Forward Checking and Constraint Propagation (1) Suppose John has already taken 19-601 towards his Information Warfare Requirement and 15-211 towards his Algorithms Requirement. Use forward checking and constraint propagation to determine other classes he must take to graduate Can he graduate?

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Forward Checking and Constraint Propagation (1) AR 1 has been set to 15-211 and IWR has been set to 19-601. Forward checking can then be used as follows: AR 2 domain goes from 15-212,15-381,15-681,21-484 to 15-212 due to IAR. MLR domain goes to 80-310 due to IAR. CR goes to 21-484,70-311 due to BAR. Constraint propagation can then MLR domain has a single member, so we select 80-310. AR 2 also has a single member, so we can select 15-212. So we have a schedule which satisfies AR 1, AR 2, MLR, and CR. But to satisfy the CR we have to select between 21-484 and 70-311 (we can’t pick both) we would need to do some search here to pick between them

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