We identify a new and important global (or non-binary) constraint. This constraint ensures that the values taken by two vectors of variables, when viewed as multisets, are ordered. This constraint is useful for a number of different applications including breaking symmetry and fuzzy constraint satisfaction. We propose and implement an efficient linear time algorithm for enforcing generalised arc consistency on such a multiset ordering constraint. Experimental results on several problem domains show considerable promise.

Many real life optimization problems contain both hard and soft constraints, as well as qualitative conditional preferences. However, there is no single formalism to specify all three kinds of information. We therefore propose a framework, based on both CP-nets and soft constraints, that handles both hard and soft constraints as well as conditional preferences efficiently and uniformly. We study the complexity of testing the consistency of preference statements, and show how soft constraints can faithfully approximate the semantics of conditional preference statements whilst improving the computational complexity.

We show that some common and important global constraints like ALL-DIFFERENT and GCC can be decomposed into simple arithmetic constraints on which we achieve bound or range consistency, and in some cases even greater pruning. These decompositions can be easily added to new solvers. They also provide other constraints with access to the state of the propagator by sharing of variables. Such sharing can be used to improve propagation between constraints. We report experiments with our decomposition in a pseudo-Boolean solver.

We show that tools from circuit complexity can be used to study decompositions of global constraints. In particular, we study decompositions of global constraints into conjunctive normal form with the property that unit propagation on the decomposition enforces the same level of consistency as a specialized propagation algorithm. We prove that a constraint propagator has a a polynomial size decomposition if and only if it can be computed by a polynomial size monotone Boolean circuit. Lower bounds on the size of monotone Boolean circuits thus translate to lower bounds on the size of decompositions of global constraints. For instance, we prove that there is no polynomial sized decomposition of the domain consistency propagator for the ALLDIFFERENT constraint.

Commonsense reasoning, in particular qualitative spatial and temporal reasoning (QSTR), provides flexible and intuitive methods for reasoning about vague and uncertain information including spatial orientation, topology and proximity.  Despite a number of theoretical advances in QSTR, there are relatively few applications that employ these methods.  The central problem is a significant lack of application level standards and validation methods for supporting developers in adapting and integrating QSTR with their domain specific qualitative spatial and temporal models.  To address this we present a significantly novel methodology for QSTR application validation, inspired by research in software engineering.  In this paper we focus on unit testing, and adapt the software engineering strategy of defining boundary cases.  We present two critical boundary concepts, a methodology for isolating the units under testing from other parts of the model, and methods to assist the designer in integrating our critical boundary unit testing approach with a broader validation plan.

Planning problems deal with finding a sequence of actions that transfer the initial state of the world into a desired state. Frequently such problems are solved by dedicated algorithms but there exist planners based on translating the planning problem into a different formalism such as constraint satisfaction or Boolean satisfiability and using a general solver for this formalism. The paper describes how to enhance existing constraint models of planning problems by using techniques such as symmetry breaking (dominance rules), singleton consistency, and lifting.

In version 2.0, IBM ILOG CP Optimizer has been extended by the introduction of scheduling support based on the concept of optional interval variables. This paper formally describes the new modeling language features available to the users of CP Optimizer for resource-based scheduling. We show that the new language is flexible enough to model problems never before addressed by CP scheduling engines, as well as naturally describing classical scheduling problems found in the literature. This modeling power is based on a small number of general concepts such as intervals, sequences and functions. This makes the modeling language simple, clear and easy to learn, while maintaining the high-level structural aspects of the scheduling model.

Vincent Aleven Intelligent tutoring systems (ITS) are highly effective in supporting student learning, but are difficult to build. The Cognitive Tutor Authoring Tools (CTAT) project started over 6 years ago with the goals of making it easier for experienced programmers, and possible for non-programmers to create an ITS. CTAT supports tutor building through programming by demonstration, an approach that has been successful in a range of application areas, but that has been applied to only a very limited degree to ITS authoring. Using CTAT, an author creates a tutor by demonstrating correct and incorrect problem solving behaviors, rather than by writing code. The resulting tutors, called exampletracing tutors, evaluate student behavior by flexibly comparing it against the demonstrated problem-solving examples.

We introduce a new tractable temporal constraint language, which strictly contains the Ord-Horn language of Buerkert and Nebel and the class of AND/OR precedence constraints. The algorithm we present for this language decides whether a given set of constraints is consistent in time that is quadratic in the input size. We also prove that (unlike Ord-Horn) this language cannot be solved by Datalog or by establishing local consistency.

In this paper a new dynamic subsumption technique for Boolean CNF formulae is proposed. It exploits simple and sufficient conditions to detect during conflict analysis, clauses from the original formula that can be reduced by subsumption. During the learnt clause derivation, and at each step of the resolution process, we simply check for backward subsumption between the current resolvent and clauses from the original formula and encoded in the implication graph. Our approach give rise to a strong and dynamic simplification technique that exploits learning to eliminate literals from the original clauses. Experimental results show that the integration of our dynamic subsumption approach within the state-of-the-art SAT solvers Minisat and Rsat achieves interesting improvements particularly on crafted instances.