Global Constraint Catalog: Kpure_functional

3.7.200. Pure functional dependency

A constraint for which the meaning is completely captured by one or more functional dependancies. The negation of such constraints can be directly expressed as a disjunction between the different functional dependancies. We illustrate this point on different examples:

The negation of the $𝚗𝚟𝚊𝚕𝚞𝚎$ $(n, 〈 v_{1}, v_{2}, \dots, v_{m} 〉)$ constraint is defined by $𝚗𝚟𝚊𝚕𝚞𝚎$ $(p, 〈 v_{1}, v_{2}, \dots, v_{m} 〉) \land n \neq p$ .
The negation of the $𝚌𝚘𝚖𝚖𝚘𝚗$ $(n_{1}, n_{2}, 〈 u_{1}, u_{2}, \dots, u_{p} 〉, 〈 v_{1}, v_{2}, \dots, v_{q} 〉)$ constraint is defined by $𝚌𝚘𝚖𝚖𝚘𝚗$ $(m_{1}, m_{2}, 〈 u_{1}, u_{2}, \dots, u_{p} 〉, 〈 v_{1}, v_{2}, \dots, v_{q} 〉) \land (n_{1} \neq m_{1} \lor n_{2} \neq m_{2})$ .
The negation of the $𝚎𝚕𝚎𝚖𝚎𝚗𝚝𝚜$ $(〈 𝚒𝚗𝚍𝚎𝚡 - i_{1} 𝚟𝚊𝚕𝚞𝚎 - u_{1}, 𝚒𝚗𝚍𝚎𝚡 - i_{2} 𝚟𝚊𝚕𝚞𝚎 - u_{2}, \dots, 𝚒𝚗𝚍𝚎𝚡 - i_{n} 𝚟𝚊𝚕𝚞𝚎 - u_{n} 〉, 〈 𝚒𝚗𝚍𝚎𝚡 - 1 𝚟𝚊𝚕𝚞𝚎 - v_{1}, 𝚒𝚗𝚍𝚎𝚡 - 2 𝚟𝚊𝚕𝚞𝚎 - v_{2}, \dots, 𝚒𝚗𝚍𝚎𝚡 - n 𝚟𝚊𝚕𝚞𝚎 - v_{n} 〉)$ constraint is defined by $𝚎𝚕𝚎𝚖𝚎𝚗𝚝𝚜$ $(〈 𝚒𝚗𝚍𝚎𝚡 - i_{1} 𝚟𝚊𝚕𝚞𝚎 - w_{1}, 𝚒𝚗𝚍𝚎𝚡 - i_{2} 𝚟𝚊𝚕𝚞𝚎 - w_{2}, \dots, 𝚒𝚗𝚍𝚎𝚡 - i_{n} 𝚟𝚊𝚕𝚞𝚎 - w_{n} 〉, 〈 𝚒𝚗𝚍𝚎𝚡 - 1 𝚟𝚊𝚕𝚞𝚎 - v_{1}, 𝚒𝚗𝚍𝚎𝚡 - 2 𝚟𝚊𝚕𝚞𝚎 - v_{2}, \dots, 𝚒𝚗𝚍𝚎𝚡 - n 𝚟𝚊𝚕𝚞𝚎 - v_{n} 〉) \land (u_{1} \neq w_{1} \lor u_{2} \neq w_{2} \lor \dots \lor u_{n} \neq w_{n})$ .
The negation of the $𝚜𝚘𝚛𝚝$ $(〈 u_{1}, u_{2}, \dots, u_{n} 〉, 〈 v_{1}, v_{2}, \dots, v_{n} 〉)$ constraint is defined by $𝚜𝚘𝚛𝚝$ $(〈 u_{1}, u_{2}, \dots, u_{n} 〉, 〈 w_{1}, w_{2}, \dots, w_{n} 〉) \land$ $𝚕𝚎𝚡_𝚍𝚒𝚏𝚏𝚎𝚛𝚎𝚗𝚝$ $(〈 v_{1}, v_{2}, \dots, v_{n} 〉, 〈 w_{1}, w_{2}, \dots, w_{n} 〉)$ .

Global Constraint Catalog

3. Description of the Catalogue

3.7.200. Pure functional dependency