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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