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

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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...

Asked By : Jules

Answered By : D.W.

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.

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Question Source : http://cs.stackexchange.com/questions/43569

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