Global Constraint Catalog: Cimply

5.176. imply

DESCRIPTION

LINKS

AUTOMATON

Origin

Logic

Constraint

$𝚒𝚖𝚙𝚕𝚢 (𝚅𝙰𝚁, 𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂)$

Synonyms

$𝚛𝚎𝚕$ , $𝚒𝚏𝚝𝚑𝚎𝚗$ .

Arguments

$𝚅𝙰𝚁$	$𝚍𝚟𝚊𝚛$
$𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂$	$𝚌𝚘𝚕𝚕𝚎𝚌𝚝𝚒𝚘𝚗 (𝚟𝚊𝚛 - 𝚍𝚟𝚊𝚛)$

Restrictions

𝚅𝙰𝚁 \geq 0

𝚅𝙰𝚁 \leq 1

| 𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂 | = 2

𝚛𝚎𝚚𝚞𝚒𝚛𝚎𝚍

(𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂, 𝚟𝚊𝚛)

𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂 . 𝚟𝚊𝚛 \geq 0

𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂 . 𝚟𝚊𝚛 \leq 1

Purpose

Let $𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂$ be a collection of 0-1 variables ${𝚅𝙰𝚁}_{1}, {𝚅𝙰𝚁}_{2}$ . Enforce $𝚅𝙰𝚁 = ({𝚅𝙰𝚁}_{1} \Rightarrow {𝚅𝙰𝚁}_{2})$ .

Example

(1, 〈0, 0〉)

(1, 〈0, 1〉)

(0, 〈1, 0〉)

(1, 〈1, 1〉)

Symmetry

All occurrences of 0 in $𝚅𝙰𝚁$ and in $𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂 . 𝚟𝚊𝚛$ can be set to 1.

Arg. properties

Functional dependency: $𝚅𝙰𝚁$ determined by $𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂$ .

Counting

Length ( $n$ )	2	3	4	5	6	7	8
Solutions	4	0	0	0	0	0	0

Number of solutions for $𝚒𝚖𝚙𝚕𝚢$ : domains $0 . . n$

ctrs/imply-1-tikz

ctrs/imply-2-tikz

Length (

n

)

Total

Parameter

value

Solution count for $𝚒𝚖𝚙𝚕𝚢$ : domains $0 . . n$

ctrs/imply-3-tikz

ctrs/imply-4-tikz

Systems

reifiedLeftImp in Choco, rel in Gecode, ifthenbool in JaCoP, #=> in SICStus.

implies: $𝚊𝚝𝚕𝚎𝚊𝚜𝚝_𝚗𝚟𝚊𝚕𝚞𝚎$ , $𝚜𝚘𝚏𝚝_𝚊𝚕𝚕𝚍𝚒𝚏𝚏𝚎𝚛𝚎𝚗𝚝_𝚌𝚝𝚛$ .

Keywords

characteristic of a constraint: automaton, automaton without counters, reified automaton constraint.

constraint arguments: pure functional dependency.

constraint network structure: Berge-acyclic constraint network.

constraint type: Boolean constraint.

filtering: arc-consistency.

modelling: functional dependency.

Automaton: Figure 5.176.1 depicts the automaton associated with the $𝚒𝚖𝚙𝚕𝚢$ constraint. To the first argument $𝚅𝙰𝚁$ of the $𝚒𝚖𝚙𝚕𝚢$ constraint corresponds the first signature variable. To each variable ${𝚅𝙰𝚁}_{i}$ of the second argument $𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂$ of the $𝚒𝚖𝚙𝚕𝚢$ constraint corresponds the next signature variable. There is no signature constraint.

Figure 5.176.1. Automaton of the $𝚒𝚖𝚙𝚕𝚢$ constraint

Figure 5.176.2. Hypergraph of the reformulation corresponding to the automaton of the $𝚒𝚖𝚙𝚕𝚢$ constraint

Global Constraint Catalog

5. Global Constraint Catalogue

5.176. imply

Figure 5.176.1. Automaton of the $𝚒𝚖𝚙𝚕𝚢$ constraint

Figure 5.176.2. Hypergraph of the reformulation corresponding to the automaton of the $𝚒𝚖𝚙𝚕𝚢$ constraint

Global Constraint Catalog

5. Global Constraint Catalogue

5.176. imply

Figure 5.176.1. Automaton of the 𝚒𝚖𝚙𝚕𝚢 constraint

Figure 5.176.2. Hypergraph of the reformulation corresponding to the automaton of the 𝚒𝚖𝚙𝚕𝚢 constraint

Figure 5.176.1. Automaton of the $𝚒𝚖𝚙𝚕𝚢$ constraint

Figure 5.176.2. Hypergraph of the reformulation corresponding to the automaton of the $𝚒𝚖𝚙𝚕𝚢$ constraint