04-01-Constraint-Satisfaction.pdf

# 04-01-Constraint-Satisfaction.pdf - Constraint Satisfaction...

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Constraint Satisfaction CSE 440

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Today I Constraint Satisfaction I Backtracking Search
What is Search For? I Given assumptions about the world: a single agent, deterministic actions, fully observed state, discrete state space

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What is Search For? I Given assumptions about the world: a single agent, deterministic actions, fully observed state, discrete state space I Planning: sequences of actions I The path to the goal is the important thing I Paths have various costs, depths I Heuristics give problem-specific guidance
What is Search For? I Given assumptions about the world: a single agent, deterministic actions, fully observed state, discrete state space I Planning: sequences of actions I The path to the goal is the important thing I Paths have various costs, depths I Heuristics give problem-specific guidance I Identification: assignments to variables I The goal itself is important, not the path I All paths at the same depth (for some formulations) I CSPs are a specialized class of identification problems

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Constraint Satisfaction Problems
What are Constraint Satisfaction Problems? I Standard search problems: I State is a “black box”: arbitrary data structure I Goal test can be any function over states I Successor function can also be anything

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What are Constraint Satisfaction Problems? I Standard search problems: I State is a “black box”: arbitrary data structure I Goal test can be any function over states I Successor function can also be anything I Constraint satisfaction problems (CSPs): I A special subset of search problems I State is defined by variables X i with values from a domain D (sometimes D depends on i ) I Goal test is a set of constraints specifying allowable combinations of values for subsets of variables
What are Constraint Satisfaction Problems? I Standard search problems: I State is a “black box”: arbitrary data structure I Goal test can be any function over states I Successor function can also be anything I Constraint satisfaction problems (CSPs): I A special subset of search problems I State is defined by variables X i with values from a domain D (sometimes D depends on i ) I Goal test is a set of constraints specifying allowable combinations of values for subsets of variables I Allows useful general-purpose algorithms with more power than standard search algorithms

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CSP Example
Example: Map Coloring I Variables: WA , NT , Q , NSW , V , SA , T

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Example: Map Coloring I Variables: WA , NT , Q , NSW , V , SA , T I Domains: D = red, green, blue
Example: Map Coloring I Variables: WA , NT , Q , NSW , V , SA , T I Domains: D = red, green, blue I Constraints: adjacent regions must have different colors

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Example: Map Coloring I Variables: WA , NT , Q , NSW , V , SA , T I Domains: D = red, green, blue I Constraints: adjacent regions must have different colors I Implicit: WA 6 = NT
Example: Map Coloring I Variables: WA , NT , Q , NSW , V , SA , T I Domains: D = red, green, blue I Constraints: adjacent regions must have different colors I Implicit: WA 6 = NT I Explicit: ( WA, NT ) ( red, green ) , ( red, blue ) , . . .

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Example: Map Coloring I Variables: WA , NT , Q , NSW , V , SA , T I Domains: D = red, green, blue
• Winter '15
• Constraint satisfaction, Constraint satisfaction problem

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