Download CSPs & Logic-based Inference - Computer Science & Engineering

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
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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
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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,
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Constraint Satisfaction Problem Example
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1. Backtracking Search
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2. Local Search
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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
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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?
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Wumpus World
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Wumpus World
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Wumpus World
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Wumpus World