3.7.122. Hybrid-consistency

Denotes that, for a given constraint involving both domain and set variables, there is a filtering algorithm that ensures hybrid-consistency. A constraint ctr defined on the distinct domain variables V 1 d ,⋯,V n d and the distinct set variables V n+1 s ,⋯,V m s is hybrid-consistent if and only if:

  • For every pair (V d ,v) such that V d is a domain variable of ctr and v∈𝑑𝑜𝑚(V d ), there exists at least one solution to ctr in which V d is assigned the value v.

  • For every pair (V s ,v) such that V s is a set variable of ctr, if v∈V s ̲ then v belongs to the set assigned to V s in all solutions to ctr and if v∈V s ¯∖V s ̲ then v belongs to the set assigned to V s in at least one solution and is excluded from this set in at least one solution.