5.68. circular_change
| DESCRIPTION | LINKS | GRAPH | AUTOMATON |
- Origin
- Constraint
- Arguments
- Restrictions
- Purpose
is the number of times that holds on consecutive variables of the collection . The last and the first variables of the collection are also considered to be consecutive.
- Example
-
In the example the changes within the collection are located between values 4 and 3, 3 and 4, 4 and 1, and 1 and 4 (i.e.,Β since the third argument of the constraint is set to , we count one change for each disequality constraint between two consecutive variables that holds). Consequently, the corresponding constraint holds since its first argument is fixed to 4.
- Typical
- Symmetries
- Arg. properties
Functional dependency: determined by and .
- See also
- Keywords
characteristic of a constraint: cyclic, automaton, automaton with counters.
constraint arguments: pure functional dependency.
constraint network structure: circular sliding cyclic(1) constraint network(2).
- Arc input(s)
- Arc generator
-
- Arc arity
- Arc constraint(s)
- Graph property(ies)
-
- Graph model
Since we are also interested in the constraint that links the last and the first variable we use the arc generator to produce the arcs of the initial graph.
PartsΒ (A) andΒ (B) of FigureΒ 5.68.1 respectively show the initial and final graph associated with the Example slot. Since we use the graph property, the arcs of the final graph are stressed in bold.
Figure 5.68.1. Initial and final graph of the constraint
(a) (b)
- Automaton
FigureΒ 5.68.2 depicts the automaton associated with the constraint. To each pair of consecutive variables of the collection corresponds a 0-1 signature variable . The following signature constraint links , and : .
Figure 5.68.2. Automaton of the constraint
Figure 5.68.3. Hypergraph of the reformulation corresponding to the automaton of the constraint
