Tobias Müller

Constructive Disjunction Revisited

Finite Domain Programming is a technique for solving combinatorial problems like planning, scheduling, configuration or timetabling. Inevitably, these problems employ disjunctive constraints. A rather new approach to model those constraints is constructive disjunction, whereby common information is lifted from the alternatives, aiming for stronger pruning of the search space. We show where constructive disjunction provides for stronger pruning and where it fails to do so. For several problems, including a real-world college timetabling application, benefits ↭d limitations of constructive disjunction are exemplified. As an experimental platform we use the concurrent constraint language Oz.

Practical Investigation of Constraints with Graph Views

Combinatorial problems can be efficiently tackled with constraint programming systems. The main tasks of the development of a constraint-based application are modeling the problem at hand and subsequently implementing that model. Typically, erroneous behavior of a constraint-based application is caused by either the model or the implementation (or both of them). Current constraint programming systems provide limited debugging support for modeling and implementing a problem. This paper proposes the Constraint Investigator, an interactive tool for debugging the model and the implementation of a constraint-based application. In particular, the Investigator is targeted at problems like wrong, void, or partial solutions. A graph metaphor is used to reflect the constraints in the solver and to present them to the user. The paper shows that this metaphor is intuitive and proposes appraoches to deal with real-life problem sizes. The Investigator has been implemented in Mozart Oz and complements other constraint programming tools as an interactive visual search engine, forming the base for an integrated constraint debugging environment.

Integrating Constraint Solving into Proof Planning

In proof planning mathematical objects with theory-specific properties have to be constructed. More often than not, mere unification offers little support for this task. However, the integration of constraint solvers into proof planning can sometimes help solving this problem. We present such an integration and discover certain requirements to be met in order to integrate the constraint solver’s efficient activities in a way that is correct and sufficient for proof planning. We explain how the requirements can be met by n extension of the constraint solving technology and describe their implementation in the constraint solver \({\mathcal C}o{\cal SIE}\).

Promoting Constraints to First-Class Status

This paper proposes to promote constraints to first-class status. In contrast to constraint propagation, which performs inference on values of variables, first-class constraints allow reasoning about the constraints themselves. This lets the programmer access the current state of a constraint and control a constraints behavior directly, thus making powerful new programming and inference techniques possible, as the combination of constraint propagation and rewriting constraints a la term rewriting. First-class constraints allow for true meta constraint programming. Promising applications in the field of combinatorial optimization include early unsatisfiability detection, constraint reformulation to improve propagation, garbage collection of redundant but not yet entailed constraints, and finding minimal inconsistent subsets of a given set of constraints for debugging immediately failing constraint programs. We demonstrate the above-mentioned applications by means of examples. The experiments were done with Mozart Oz but can be easily ported to other constraint solvers.