1. CS182 Intelligent Machines: Reasoning, Actions and Plans Section 4

2. Reminder -- 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

3. 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

4. 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.

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

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

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

8. Depth-First Search for CSP AR_1 = 15-211 AR_2 = 15-212 MLR = 15-381MLR = 15-681MLR = 80-310 CR = 21-484CR = 70-122CR = 70-311CR = 21-484CR = 70-122CR = 70-311CR = 21-484 IWR= 15-381 IWR= 19-601 IWR= 15-381 IWR= 19-601 IWR= 15-381 IWR= 19-601 IWR= 15-381 IWR= 19-601 IWR= 15-381 AR_1: 15-211, 15-212, 15-381, 15-681, 21-484 AR_2: 15-211, 15-212, 15-381, 15-681, 21-484 MLR: 15-381, 15-681, 80-310 CR: 21-484, 70-122, 70-311 IWR: 15-381, 19-601 AR: (15-211 & 15-212) |(15-211 & 15-381) |(15-681 &21-484) MLR: : 15-381 OR 15-681 OR 80-310 CR: 21-484 OR 70-311 OR 70-122 IWR: 15-381 OR 19-601 Only one of 15-381, 15-681, and 19-601; Only one of 15-211 and 70-122; Only one of 21-484 and 70-311 No double credit

9. Depth-First Search + Forward Checking AR_1 = 15-211 AR_2 = 15-212 MLR = 15-381MLR = 15-681 AR_1: 15-211, 15-212, 15-381, 15-681, 21-484 AR_2: 15-211, 15-212, 15-381, 15-681, 21-484 MLR: 15-381, 15-681, 80-310 CR: 21-484, 70-122, 70-311 IWR: 15-381, 19-601 Backtrack here! … AR: (15-211 & 15-212) |(15-211 & 15-381) |(15-681 &21-484) MLR: : 15-381 OR 15-681 OR 80-310 CR: 21-484 OR 70-311 OR 70-122 IWR: 15-381 OR 19-601 Only one of 15-381, 15-681, and 19-601; Only one of 15-211 and 70-122; Only one of 21-484 and 70-311 No double credit

10. Course Scheduling with Propositional Logic A simplified version of course scheduling (in natural language): Communications Requirement: 21-484 OR 70-311 OR 70-122 Information Warfare Requirement: 15-381 OR 19- 601 Students can graduate as long as both requirements are satisfied

11. Representation in Propositional Logic

12. Theorem Proving A student took 70-311 and 15-381 but not 19- 601, prove that this student can graduate

13. A Resolution Algorithm

14. Theorem Proving with Resolution

15. Step 1: Convert into CNF

16. Step 2: Apply Resolution Rules CR IWR {} Graduate

17. WalkSAT (Clauses, max_flips, p) Choose a random model m (random assignment to each variable) If m satisfies constraints – Return m Else, while num_flips < max_flips – With probability p choose a variable to “flip” randomly – With probability 1-p choose flip the variable that minimizes number of unsatisfied constraints Return null

18. “WalkSAT” for course scheduling What does it mean to “flip”? What are the input clauses? Example: – Assume our random assignment is just the first value from the domain for each: AR_1: 15-211,AR_2: 15-211, MLR: 15-381, CR: 21-484, IWR: 15-381 – If we draw random<p, we choose randomly on of these to flip (for example, flip 15-211 to 15-212 – If we draw random>p we need to find the change that will minimize the number of unsatisfied constraints (try at home)