Constraint satisfaction problems
are defined by…

a set of
variables
X
:
{WA, NT, QLD, NSW, VA, SA, TA}

a set of
domains
D
i
(possible values for variable x
i
):
D
WA
= {red, blue, green}

a set of
constraints
C
:
{
(WA,NT)
,
WA
≠
NT
,
(WA,QLD), WA
≠
QLD ,…}
scope
relation
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CS440/ECE448: Intro AI
States and solutions
Each
state
is a
complete or partial assignment
of values to variables:
state35 = {WA=red, NT=blue, QLD= green, NSW= red,
VA= green, SA= blue, TA= red};
state23 = {WA = red}
Legal assignments
don
ʼ
t violate any constraints.
Solutions
are complete legal assignments
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CS440/ECE448: Intro AI
Binary constraints:
constraint graph
QLD
NT
NSW
VA
TA
SA
WA
CS440/ECE448: Intro AI
7
Consistency
Node consistency:
X is nodeconsistent iff
each element in D
X
satisfies unary constraints on X
Arc consistency:
X is arcconsistent iff
for each C(X, Y) and for each
x
D
X
there is a
y
D
Y
such that the assignment {X=x, Y=y} satisfies C(X,Y).
Path consistency:
{X,Y} are path consistent wrt. Z iff
for every x
D
X
and y
D
X
there is a z
D
Z
such that the
assignment {X=x,Y=y,Z=z} satisfies C(X,Z) and C(Y,Z)
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CS440/ECE448: Intro AI