5.174. ith_pos_different_from_0

DESCRIPTIONLINKSAUTOMATON
Origin

N.Β Beldiceanu

Constraint

πš’πšπš‘_πš™πš˜πšœ_πšπš’πšπšπšŽπš›πšŽπš—πš_πšπš›πš˜πš–_0(π™Έπšƒπ™·,π™Ώπ™Ύπš‚,πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚)

Arguments
π™Έπšƒπ™·πš’πš—πš
π™Ώπ™Ύπš‚πšπšŸπšŠπš›
πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚πšŒπš˜πš•πš•πšŽπšŒπšπš’πš˜πš—(πšŸπšŠπš›-πšπšŸπšŠπš›)
Restrictions
π™Έπšƒπ™·β‰₯1
π™Έπšƒπ™·β‰€|πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚|
π™Ώπ™Ύπš‚β‰₯π™Έπšƒπ™·
π™Ώπ™Ύπš‚β‰€|πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚|
πš›πšŽπššπšžπš’πš›πšŽπš(πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚,πšŸπšŠπš›)
Purpose

π™Ώπ™Ύπš‚ is the position of the π™Έπšƒπ™· th non-zero item of the sequence of variables πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚.

Example
(2,4,3,0,0,8,6)

The πš’πšπš‘_πš™πš˜πšœ_πšπš’πšπšπšŽπš›πšŽπš—πš_πšπš›πš˜πš–_0 constraint holds since 4 corresponds to the position of the 2th non-zero item of the sequence 3 0 0 8 6.

Typical
|πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚|>1
πš›πšŠπš—πšπšŽ(πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚.πšŸπšŠπš›)>1
πšŠπšπš•πšŽπšŠπšœπš(1,πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚,0)
Symmetry

An occurrence of a value of πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚.πšŸπšŠπš› that is different from 0 can be replaced by any other value that is also different from 0.

Keywords

characteristic of a constraint: joker value, automaton, automaton with counters.

constraint network structure: alpha-acyclic constraint network(3).

constraint type: data constraint.

modelling: table.

Automaton

FigureΒ 5.174.1 depicts the automaton associated with the πš’πšπš‘_πš™πš˜πšœ_πšπš’πšπšπšŽπš›πšŽπš—πš_πšπš›πš˜πš–_0 constraint. To each variable πš…π™°πš i of the collection πš…π™°πšπ™Έπ™°π™±π™»π™΄πš‚ corresponds a 0-1 signature variable πš‚ i . The following signature constraint links πš…π™°πš i and πš‚ i : πš…π™°πš i =0β‡”πš‚ i .

Figure 5.174.1. Automaton of the πš’πšπš‘_πš™πš˜πšœ_πšπš’πšπšπšŽπš›πšŽπš—πš_πšπš›πš˜πš–_0 constraint
ctrs/ith_pos_different_from_01
Figure 5.174.2. Hypergraph of the reformulation corresponding to the automaton of the πš’πšπš‘_πš™πš˜πšœ_πšπš’πšπšπšŽπš›πšŽπš—πš_πšπš›πš˜πš–_0 constraint
ctrs/ith_pos_different_from_02