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05_CSP - Moving to a different formalism SEND MORE-MONEY...

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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 : 1 2 3 {0 , ..., 9} ; {0 , ..., 9} ; 0 {0 , ..., 9} ; {0 , ..., 9} ; {0 , ..., 9} ; {0 , ..., 9} ; {0 , ..., 9} ; {0 , ..., 9} ; {0 , ..., 9} ; T W F U R X X X TWO + TWO FOUR Auxiliary variables 1 1 2 2 3 3 0 0 1 0 * 1 0 * 1 0 * e a c h le tte r h a s a d iffe re n t d ig it R X X W W U X X T T O X X F C o n s tr a in ts : (F T ,F U ,e tc .); Constraint Hypergraph TWO + TWO FOUR T U W R O 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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