5.30. and
DESCRIPTION | LINKS | AUTOMATON |
- Origin
Logic
- Constraint
- Synonym
.
- Arguments
- Restrictions
- Purpose
Let be a collection of 0-1 variables . Enforce .
- Example
-
- Symmetry
Items of are permutable.
- Arg. properties
Functional dependency: determined by .
Extensible wrt. when .
Aggregate: , .
- Counting
-
Length () 2 3 4 5 6 7 8 Solutions 4 8 16 32 64 128 256 Number of solutions for : domains
Length () 2 3 4 5 6 7 8 Total 4 8 16 32 64 128 256 Parameter value 0 3 7 15 31 63 127 255 1 1 1 1 1 1 1 1 Solution count for : domains
- Systems
reifiedAnd in Choco, rel in Gecode, andbool in JaCoP, #/\ in SICStus.
- See also
common keyword: , , , , , , Β (Boolean constraint).
implies: , , , .
- Keywords
characteristic of a constraint: automaton, automaton without counters, reified automaton constraint.
constraint arguments: pure functional dependency.
constraint network structure: Berge-acyclic constraint network.
- Cond. implications
- Automaton
FigureΒ 5.30.1 depicts a first deterministic automaton without counter associated with the constraint. To the first argument of the constraint corresponds the first signature variable. To each variable of the second argument of the constraint corresponds the next signature variable. There is no signature constraint.
Figure 5.30.1. Counter free automaton of the constraint (the transition represents the fact that at least one variable should be set to 0 when , while the transition represents the fact that all should be set to 1 when )
Figure 5.30.2. Hypergraph of the reformulation corresponding to the automaton of the constraint
FigureΒ 5.30.3 depicts a second deterministic automaton with one counter associated with the constraint, where the argument is unified to the final value of the counter.
Figure 5.30.3. Automaton (with one counter) of the constraint
Figure 5.30.4. Hypergraph of the reformulation corresponding to the automaton (with one counter) of the constraint (since all states of the automaton are accepting there is no restriction on the last variable )