I'm trying to solve problem 6.6 from the book Artificial Intelligence: A Modern Approach, by Peter Norvig and Stuart Russell.
This is in the context of Constraint Satisfaction Problem and how you can re-formulate some problems with the constraints expressed as a bunch of binary constraints to use the generalized solver CSP algorithm.
But I'm stuck with that exercise, I can't sketch a demonstration.
6.6 Show how a single ternary constraint such as "A + B = C" can be turned into three binary constraints by using an auxiliary variable. You may assume finite domains.
(Hint: Consider a new variable that takes on values that are pairs of others values, and consider constraints such as "X is the first element of the pair Y.") Next, show how constraints can be eliminated by altering the domain of variables. This completes the demonstration that any CSP can be transformed into a CSP with only binary constraints.