1. CS482/682 Artificial Intelligence Lecture 8: Constraint Satisfaction Problems and Logic-based Inference 17 September 2009 Instructor: Kostas Bekris Computer Science & Engineering, University of Nevada, Reno

2. 482/682 Search-based Problems Search Problems Given the state-space, a start state and a successor function Find a goal state Local SearchClassical Search Hill-climbing Hill-climbing with random restarts Simulated Annealing Local Beam Search Genetic Algorithms Uninformed BFS Uniform-First DFS Iterat.-Deep. DFS Bidirectional Informed Best-First Search Greedy BestFS A* Constraint Satisfaction Problems

3. 482/682 Constraint-Satisfaction Problems Discrete and Finite Domains Map-Coloring 8-queens puzzle Boolean CSPs Satisfiability problems (prototypical NP-Complete problem) Discrete and Infinite Domains Scheduling over the set of integers (e.g., all the days after today) Continuous Domains Scheduling over continuous time Linear Programming problems  Constraints are linear inequalities over the variables Additional examples: crossword puzzles, cryptography problems, Sudoku and many classical NP-Complete problems: clique problems, vertex-cover, traveling salesman, subset-sum, hamiltonian-cycle

4. 482/682 Constraint Satisfaction Problem Example

5. 482/682 1. Backtracking Search

6. 482/682 2. Local Search

7. 482/682 1. Backtracking: Forward Checking WANTQNSWVSAT InitiallyRGB After WA=R RG BRGB G BRGB After Q = GRBGR BRGBB After V=BRBGRBRGB

8. 482/682 1. Backtracking: Intelligent Backjumping Assume WA=red and NSW =red, then assign T, NT, Q, SA SA will cause a conflict, whatever we do... Where should the algorithm backjump?

9. 482/682 Wumpus World

10. 482/682 Wumpus World

11. 482/682 Wumpus World

12. 482/682 Wumpus World