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Erschienen in:
2009 | OriginalPaper | Buchkapitel
Four Subareas of the Theory of Constraints, and Their Links
verfasst von : Albert Atserias
Erschienen in: Mathematical Foundations of Computer Science 2009
Verlag: Springer Berlin Heidelberg
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Let
V
= {
x
1
,...,
x
n
} be a set of variables that range over a set of values
D
= {
d
1
,...,
d
q
}. A constraint is an expression of the type
$R(x_{i_1},\ldots,x_{i_r})$
, where
R
⊆
D
r
is a relation on the domain set
D
and
$x_{i_1},\ldots,x_{i_r}$
are variables in
V
. The space of assignments, or configurations, is the set of all mappings
σ
:
V
→
D
. We say that
σ
satisfies the constraint
$R(x_{i_1},\ldots,x_{i_r})$
if
$(\sigma(x_{i_1}),\ldots,\sigma(x_{i_r})) \in R$
. Otherwise we say that it falsifies it. On a given
system of constraints
we face a number of important computational problems.