Global Constraint Catalog: Cequivalent

5.154. equivalent

DESCRIPTION

LINKS

AUTOMATON

Origin

Logic

Constraint

$𝚎𝚚𝚞𝚒𝚟𝚊𝚕𝚎𝚗𝚝 (𝚅𝙰𝚁, 𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂)$

Synonym

$𝚎𝚚$ .

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 $𝚅𝙰𝚁 = ({𝚅𝙰𝚁}_{1} \Leftrightarrow {𝚅𝙰𝚁}_{2})$ .

Example

(1, 〈0, 0〉)

(0, 〈0, 1〉)

(0, 〈1, 0〉)

(1, 〈1, 1〉)

Symmetries

Items of $𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂$ are permutable.
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 $𝚎𝚚𝚞𝚒𝚟𝚊𝚕𝚎𝚗𝚝$ : domains $0 . . n$

ctrs/equivalent-1-tikz

ctrs/equivalent-2-tikz

Length (

n

)

Total

Parameter

value

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

ctrs/equivalent-3-tikz

ctrs/equivalent-4-tikz

Systems

ifOnlyIf in Choco, rel in Gecode, eqbool in JaCoP, #<=> in SICStus.

implies: $𝚊𝚝𝚕𝚎𝚊𝚜𝚝_𝚗𝚟𝚊𝚕𝚞𝚎$ , $𝚜𝚘𝚏𝚝_𝚊𝚕𝚕_𝚎𝚚𝚞𝚊𝚕_𝚖𝚒𝚗_𝚌𝚝𝚛$ , $𝚜𝚘𝚏𝚝_𝚊𝚕𝚕𝚍𝚒𝚏𝚏𝚎𝚛𝚎𝚗𝚝_𝚌𝚝𝚛$ .

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 5.154.1 depicts the automaton associated with the $𝚎𝚚𝚞𝚒𝚟𝚊𝚕𝚎𝚗𝚝$ constraint. To the first argument $𝚅𝙰𝚁$ of the $𝚎𝚚𝚞𝚒𝚟𝚊𝚕𝚎𝚗𝚝$ constraint corresponds the first signature variable. To each variable ${𝚅𝙰𝚁}_{i}$ of the second argument $𝚅𝙰𝚁𝙸𝙰𝙱𝙻𝙴𝚂$ of the $𝚎𝚚𝚞𝚒𝚟𝚊𝚕𝚎𝚗𝚝$ constraint corresponds the next signature variable. There is no signature constraint.

Figure 5.154.1. Automaton of the $𝚎𝚚𝚞𝚒𝚟𝚊𝚕𝚎𝚗𝚝$ constraint

Figure 5.154.2. Hypergraph of the reformulation corresponding to the automaton of the $𝚎𝚚𝚞𝚒𝚟𝚊𝚕𝚎𝚗𝚝$ constraint

Global Constraint Catalog

5. Global Constraint Catalogue

5.154. equivalent

Figure 5.154.1. Automaton of the $𝚎𝚚𝚞𝚒𝚟𝚊𝚕𝚎𝚗𝚝$ constraint

Figure 5.154.2. Hypergraph of the reformulation corresponding to the automaton of the $𝚎𝚚𝚞𝚒𝚟𝚊𝚕𝚎𝚗𝚝$ constraint

Global Constraint Catalog

5. Global Constraint Catalogue

5.154. equivalent

Figure 5.154.1. Automaton of the 𝚎𝚚𝚞𝚒𝚟𝚊𝚕𝚎𝚗𝚝 constraint

Figure 5.154.2. Hypergraph of the reformulation corresponding to the automaton of the 𝚎𝚚𝚞𝚒𝚟𝚊𝚕𝚎𝚗𝚝 constraint

Figure 5.154.1. Automaton of the $𝚎𝚚𝚞𝚒𝚟𝚊𝚕𝚎𝚗𝚝$ constraint

Figure 5.154.2. Hypergraph of the reformulation corresponding to the automaton of the $𝚎𝚚𝚞𝚒𝚟𝚊𝚕𝚎𝚗𝚝$ constraint