## 5.283. not_in

Origin
Constraint

$\mathrm{\pi \pi \pi }_\mathrm{\pi \pi }\left(\mathrm{\pi  \pi °\pi },\mathrm{\pi  \pi °\pi »\pi \pi ΄\pi }\right)$

Arguments
 $\mathrm{\pi  \pi °\pi }$ $\mathrm{\pi \pi \pi \pi }$ $\mathrm{\pi  \pi °\pi »\pi \pi ΄\pi }$ $\mathrm{\pi \pi \pi \pi \pi \pi \pi \pi \pi \pi }\left(\mathrm{\pi \pi \pi }-\mathrm{\pi \pi \pi }\right)$
Restrictions
 $\mathrm{\pi \pi \pi \pi \pi \pi \pi \pi }$$\left(\mathrm{\pi  \pi °\pi »\pi \pi ΄\pi },\mathrm{\pi \pi \pi }\right)$ $\mathrm{\pi \pi \pi \pi \pi \pi \pi \pi }$$\left(\mathrm{\pi  \pi °\pi »\pi \pi ΄\pi },\mathrm{\pi \pi \pi }\right)$
Purpose

Enforce $\mathrm{\pi  \pi °\pi }$ to be assigned a value different from the values of the $\mathrm{\pi  \pi °\pi »\pi \pi ΄\pi }$ collection.

Example
$\left(2,β©1,3βͺ\right)$

The constraint $\mathrm{\pi \pi \pi }_\mathrm{\pi \pi }$ holds since the value of its first argument $\mathrm{\pi  \pi °\pi }=2$ does not occur within the collection $\beta ©1,3\beta ͺ$.

Typical
$|\mathrm{\pi  \pi °\pi »\pi \pi ΄\pi }|>1$
Symmetries
• Items of $\mathrm{\pi  \pi °\pi »\pi \pi ΄\pi }$ are permutable.

• One and the same constant can be added to $\mathrm{\pi  \pi °\pi }$ as well as to the $\mathrm{\pi \pi \pi }$ attribute of all items of $\mathrm{\pi  \pi °\pi »\pi \pi ΄\pi }$.

Arg. properties

Contractible wrt. $\mathrm{\pi  \pi °\pi »\pi \pi ΄\pi }$.

Remark

Entailment occurs immediately after posting this constraint and removing all values in $\mathrm{\pi  \pi °\pi »\pi \pi ΄\pi }$ from $\mathrm{\pi  \pi °\pi }$.

Systems

notMember in Choco, rel in Gecode.

Used in
Keywords
Derived Collection
$\mathrm{\pi \pi \pi }\left(\mathrm{\pi  \pi °\pi \pi Έ\pi °\pi ±\pi »\pi ΄\pi }-\mathrm{\pi \pi \pi \pi \pi \pi \pi \pi \pi \pi }\left(\mathrm{\pi \pi \pi }-\mathrm{\pi \pi \pi \pi }\right),\left[\mathrm{\pi \pi \pi \pi }\left(\mathrm{\pi \pi \pi }-\mathrm{\pi  \pi °\pi }\right)\right]\right)$
Arc input(s)

$\mathrm{\pi  \pi °\pi \pi Έ\pi °\pi ±\pi »\pi ΄\pi }$ $\mathrm{\pi  \pi °\pi »\pi \pi ΄\pi }$

Arc generator
$\mathrm{\pi \pi  \pi \pi ·\pi \pi Ά\pi }$$\beta ¦\mathrm{\pi \pi \pi \pi \pi \pi \pi \pi \pi \pi }\left(\mathrm{\pi \pi \pi \pi \pi \pi \pi \pi \pi },\mathrm{\pi \pi \pi \pi \pi \pi }\right)$

Arc arity
Arc constraint(s)
$\mathrm{\pi \pi \pi \pi \pi \pi \pi \pi \pi }.\mathrm{\pi \pi \pi }=\mathrm{\pi \pi \pi \pi \pi \pi }.\mathrm{\pi \pi \pi }$
Graph property(ies)
$\mathrm{\pi \pi \pi \pi }$$=0$

Graph model

FigureΒ 5.283.1 shows the initial graph associated with the Example slot. Since we use the $\mathrm{\pi \pi \pi \pi }=0$ graph property the corresponding final graph is empty.

Signature

Since 0 is the smallest number of arcs of the final graph we can rewrite $\mathrm{\pi \pi \pi \pi }=0$ to $\mathrm{\pi \pi \pi \pi }\beta €0$. This leads to simplify $\underset{Μ²}{\stackrel{Β―}{\mathrm{\pi \pi \pi \pi }}}$ to $\underset{Μ²}{\mathrm{\pi \pi \pi \pi }}$.

Automaton

FigureΒ 5.283.2 depicts the automaton associated with the $\mathrm{\pi \pi \pi }_\mathrm{\pi \pi }$ constraint. Let ${\mathrm{\pi  \pi °\pi »}}_{i}$ be the $\mathrm{\pi \pi \pi }$ attribute of the ${i}^{th}$ item of the $\mathrm{\pi  \pi °\pi »\pi \pi ΄\pi }$ collection. To each pair $\left(\mathrm{\pi  \pi °\pi },{\mathrm{\pi  \pi °\pi »}}_{i}\right)$ corresponds a 0-1 signature variable ${S}_{i}$ as well as the following signature constraint: $\mathrm{\pi  \pi °\pi }={\mathrm{\pi  \pi °\pi »}}_{i}\beta {S}_{i}$.