05_CSP - 9/18/2009 Moving to a different formalism. SEND +...

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9/18/2009 1 Constraint Satisfaction Moving to a different formalism… SEND + MORE ------ MONEY Consider state space for cryptarithmetic (e.g. DFS). Is this (DFS) how humans tackle the problem? Human problem solving appears more sophisticated ! For example, we derive new constraints on the fly. little or no search! Constraint Satisfaction Problems (CSP) A powerful representation for (discrete) search problems A Constraint Satisfaction Problem (CSP) is defined by: X is a set of n variables X 1 , X 2, …, X n each defined by a finite domain D 1 , D 2 ,…D n of possible values. C is a set of constraints C 1 , C 2 ,…, C m . Each C i involves a subset of the variables; specifies the allowable combinations of values for that subset. A solution is an assignment of values to the variables that satisfies all constraints. Cryptarithmetic as a CSP Variables : 123 {0,. .., 9}; .., 9}; 0 ..,9}; TW FUR XXX   TWO + TWO FOUR Auxiliary variables 1 12 23 3 00 1 0 * 10* each letter has a different digit RX XWWU X XTTO X XF      Constraints: (F T ,F U ,etc.);  Constraint Hypergraph TWO + TWO FOUR TUW RO F X 2 X 1 X 3 Map Coloring Problem Western Northern Territory Queensland Australia New South Wales South Australia Victoria Tasmania
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9/18/2009 2 Graph for Map Coloring Problem WA NT Q NSW SA V T Unary Constraints : Restriction on single variable Binary Constraints : Types of Constraints Restriction on pairs of variables Higher Order Constraints : Restriction on more than two variables Preferences vs. Constraints
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This note was uploaded on 05/30/2010 for the course CS 4700 taught by Professor Joachims during the Fall '07 term at Cornell University (Engineering School).

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05_CSP - 9/18/2009 Moving to a different formalism. SEND +...

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