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Computer Science & Engineering, University of Nevada, Reno CS482/682 Artificial Intelligence Lecture 8: Constraint Satisfaction Problems and Logic-based Inference 17 September 2009 Instructor: Kostas Bekris 482/682 Search-based Problems Search Problems Given the state-space, a start state and a successor function Constraint Satisfaction Problems Find a goal state Local Search Classical Search Uninformed Informed • Hill-climbing • BFS • Hill-climbing with random restarts • Uniform-First Best-First Search • Simulated Annealing • DFS Greedy BestFS • Local Beam Search • Iterat.-Deep. DFS •• A* • Genetic Algorithms • Bidirectional 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, 482/682 Constraint Satisfaction Problem Example 482/682 1. Backtracking Search 482/682 2. Local Search 482/682 1. Backtracking: Forward Checking WA NT Q NSW V SA T RGB RGB RGB RGB RGB RGB RGB R GB RGB RGB RGB GB RGB After Q = G R B G RB RGB B RGB After V=B R B G R B Initially After WA=R RGB 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? 482/682 Wumpus World 482/682 Wumpus World 482/682 Wumpus World 482/682 Wumpus World