Contractibility for Open Global Constraints
This work addresses a foundational issue in constraint programming for researchers and practitioners dealing with interleaved problem construction and solving, though it appears incremental as it builds on existing constraint theory.
The paper tackles the problem of ensuring sound filtering for open global constraints in constraint programming, where new variables can be added during execution, and provides a characterization called contractibility to determine when filtering remains sound, with demonstrations on hard and soft constraints.
Open forms of global constraints allow the addition of new variables to an argument during the execution of a constraint program. Such forms are needed for difficult constraint programming problems where problem construction and problem solving are interleaved, and fit naturally within constraint logic programming. However, in general, filtering that is sound for a global constraint can be unsound when the constraint is open. This paper provides a simple characterization, called contractibility, of the constraints where filtering remains sound when the constraint is open. With this characterization we can easily determine whether a constraint has this property or not. In the latter case, we can use it to derive a contractible approximation to the constraint. We demonstrate this work on both hard and soft constraints. In the process, we formulate two general classes of soft constraints.