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# Mychapter6 - Constraint Satisfaction Problems Click to edit Master subtitle style CHAPTER 6 Oliver Schulte SPRING2011 Outline CSP examples

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Click to edit Master subtitle style  7/7/11 CHAPTER 6 Oliver Schulte SPRING2011 Constraint Satisfaction Problems

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7/7/11 Outline CSP examples Backtracking search for CSPs Problem structure and problem decomposition Local search for CSPs
7/7/11 Environment Type Discussed In this Lecture Static Environment  CMPT 310 - Blind Search 33 Fully  Observab le Determini stic Sequential yes yes Discret Discret yes Planning heuristic  search yes Control,  cyberneti cs no no Continuous  Function  Optimization Vector Search:  Constraint  Satisfaction no yes

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7/7/11 Agent Architecture Discussed In this Lecture Content Placeholder 3  Graph-Based Search: State is  black box , no internal  structure, atomic.  Factored Representation: State is list or vector of  facts .  CSP: a fact is of the form “Variable = value”.  A model is a  structured  representation of  the world.
7/7/11 Constraint satisfaction problems (CSPs) CSP: state is defined by variables Xi with values from domain Di goal test is a set of constraints specifying  allowable  combinations of values for subsets of variables. Allows useful general-purpose algorithms with more  power than standard search algorithms. Power close to simulating Turing Machines.

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7/7/11 Example: Map-Coloring
7/7/11 CSPs (continued) An assignment is  complete  when every variable is mentioned.  solution  to a CSP is a complete assignment that satisfies all  constraints. Some CSPs require a solution that maximizes an  objective function . Constraints with continuous variables are common. Linear Constraints    linear programming.   Examples of Applications:  Airline schedules  Final Exam Scheduling.

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7/7/11 Example: Map-Coloring contd.
7/7/11 Varieties of constraints Unary constraints involve a single variable, e.g., SA 6= green Binary constraints involve pairs of variables, e.g., SA <> WA Higher-order constraints involve 3 or more variables

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7/7/11 Constraint graph Binary CSP: each constraint relates at most two  variables Constraint graph: nodes are variables, arcs show  constraints General-purpose CSP algorithms use the graph
7/7/11 Graphs and Factored Representations UBC AI Space CSP Graphs for variables (concepts, facts) capture  local  dependencies  between variables (concepts, facts). Absence of edges = independence. AI systems try to reason locally as much as possible.

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## This note was uploaded on 07/04/2011 for the course CMPT 310 taught by Professor Oliver during the Summer '11 term at Simon Fraser.

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Mychapter6 - Constraint Satisfaction Problems Click to edit Master subtitle style CHAPTER 6 Oliver Schulte SPRING2011 Outline CSP examples

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