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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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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).
 Fall '07
 JOACHIMS
 Artificial Intelligence

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