On the phase transitions of random k-constraint satisfaction problems

Constraint satisfaction has received increasing attention these years. Intense research has focused on solving all kinds of constraint satisfaction problems (CSPs). In this paper, first we propose a random CSP model, named k-CSP, that guarantees the existence of phase transitions under certain circumstances. The exact location of the phase transition is quantified and experimental results are provided to illustrate the performance of the proposed model. Second, we revise the model k-CSP to a random linear CSP by incorporating certain linear structure to constraint relations. We also prove the existence of the phase transition and exhibit its exact location for this random linear CSP model.