Automatic Algorithm Synthesis Applied to Arc Consistency : A Case Study

We are currently designing and implementing a knowledge-based automatic program generator, called Descartes. We show in this paper how Descartes applies to a specification of arc consistency and manages to “discover” an optimal worst-case algorithm for this problem. Finding and improving algorithms for arc consistency in CSPs has been the topic of active research for twenty years. After several attempts, an optimal worst-case algorithm, AC4, was published in 1986. Since then, several improvements have been performed, in particular AC6 last year, which improves the average-case complexity. We show how an optimal worst-case algorithm, though not as elegant as, but “trickier” than AC4, can be generated. Nevertheless, many difficulties remain, which we discuss. In particular, AC6, which is better in average-case complexity than AC4, remains out of reach.