The invention provides a computer-implemented method for generating a solution to a constraint satisfaction problem (CSP). The method operates to implement various steps that include defining the CSP problem by a set of variable having finite domains, and constraints defined over the variables, solving the CSP by assigning values to said variables that are consistent with the constraints and debugging the CSP solution. The debugging of the CSP solution is carried out by iteratively executing a propagator to reduce the variable domain. Augmenting the constraints is carried out to supply an explanation for particular values assigned to the variables, and constraints defined over the variable utilized in the solution.