World's most popular travel blog for travel bloggers.

# [Solved]: Contraint with three variables into three binary constraints

, ,
Problem Detail:

I'm having a hard time tackling the following problem (perhaps some key data is missing). We have a constraint:

\$A+B= C\$

One is supposed to represent this one constraint using three binary constraints. Is this even possible? No domain is given, but even if it was, I really don't see how this could be achieved...

Good question. Your instinctive reaction is quite valid: if you stick with the variables \$A,B,C\$, there is no way to introduce some set of binary constraints that will be equivalent to \$A+B=C\$ (where each constraint is only allowed to mention two of \$A,B,C\$).

The trick is to introduce new variables, or change the set of variables. If you do that, it can be done. For instance, see the reference that hengxin suggests: http://ktiml.mff.cuni.cz/~bartak/constraints/binary.html. However, it would be understandable if you feel that this is in some sense "cheating"... which might be why you didn't think of this approach.