this paper was motivated by the desire to evaluate CSP as the basis for consistency-based diagnosis. Much of the work to date in consistency-based diagnosis uses the technique of constraint-propagation [de Kleer 87], [Hamscher 91], but does not use a specific logical system as its basis. Recently, [Bond 94] uses LP (logic programming) as the basis for a diagnostic procedure. [Mackworth 92] gives a partially ordered graph which defines a hierarchy of logical systems. Because CSP (Constraint Satisfaction Problem) is both relatively mature and among the simpler logical systems available, it would be highly desirable as a basis for diagnosis. Researchers in CSP, [Dechter 90], [El Fattah 92] and in PCSP (Partial Constraint Satisfaction Problems) [Sabin 94], have addressed the use of CSP for diagnosis. This paper discusses the use of CSP as a logical system for further research in consistency-based diagnosis.

In [1, 2], Bessière and Cordier said that the AC-6 arc-consistency algorithm is optimal in time on constraint networks where nothing is known about the constraint semantics. However, in constraint networks, it is always assumed that constraints are symmetric. None of the previous algorithms achieving arc-consistency (AC-3 [5, 6], AC-4 [7], AC-6) use this property. We propose here an improved version of AC-6 (the best algorithm for arcconsistency) which uses this property. Then, we claim that our new algorithm is optimal in the number of constraint checks performed. 1. Introduction In the last five years, the number of applications using constraint networks has dramatically increased. It appears that the more constraint networks are used, the simpler the constraint satisfaction techniques involved in the applications are. In fact, a great part of real-life applications using constraint networks are limited to a forward-checking search procedure [4], or use an arc-consistency filtering a...

The paper evaluates the e ectiveness of learning for speeding up the solution of constraint satisfaction problems. It extends previous work (Dechter 1990) by introducing a new and powerful variant of learning and by presenting an extensive empirical study on much larger and more di cult problem instances. Our results show that learning can speed up backjumping when using either a xed or dynamic variable ordering. However, the improvement with a dynamic variable ordering is not as great, and for some classes of problems learning is helpful only when a limit is placed on the size of new constraints learned. 1.