CSP Forward checking with n-ary (and binary) constraints I have implemented my own CSP solver using a Backtracking algorithm.
Within the Backtracking algorithm I apply a Forward Checking algorithm (reducing domains of connected, unnasigned variables) that only works with Binary constraints.

The problem I have is that the CSP I try to solve has lots of n-ary constraints, making the FC algorithm mostly redundant. 

Is there a way to enhance or replace my FC algorithm, so it works with n-ary constraints.
Or is there a "simple" procedure to convert n-ary constraints to binary constraints?

EDIT:
Added pseudo code (attempt) of the Forward Checking algorithm:

function ForwardChecking(variable, csp) list of variables with new domains, or failure
    for each constraint in connectedConstraints(variable) do
        if connectedVariable is assigned then
            if constraint is not satisfied then
                return failure
        else 
            for each value in connectedVariable.domain do
                connectedVariable.assign(value)
                if constraint is not satisfied do
                    remove value from connectedVariable.domain
                if connectedVariable.domain.count == 0 then
                    return failure
                add connectedVariable to solution
    return solution
Instead of forward checking, try arc consistency. You run arc consistency after every assignment to reduce backtracking. 

Another further improvement would be assigning a least constraining value (LCV) to a variable with minimum value in the domain (MRV).