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Conference Paper

Atomic Set Constraints with Projection


Charatonik,  Witold
Programming Logics, MPI for Informatics, Max Planck Society;

Talbot,  Jean-Marc
Programming Logics, MPI for Informatics, Max Planck Society;

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Charatonik, W., & Talbot, J.-M. (2002). Atomic Set Constraints with Projection. In Rewriting Techniques and Applications. 13th International Conference, RTA 2002 (pp. 311-325). Berlin, Germany: Springer.

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We investigate a class of set constraints defined as atomic set constraints augmented with projection. This class subsumes some already studied classes such as atomic set constraints with left-hand side projection and INES constraints. All these classes enjoy a nice property that satisfiability can be performed in cubic time. This has be contrasted with several other classes of set constraints, such as definite set constraints and positive set constraints, for which satisfiability ranges from DEXPTIME-complete to NEXPTIME-complete. However, these latter classes allow set operators such as intersection or union which is not the case for the class studied here. In the case of atomic set constraints with projection one might expect that satisfiability remains polynomial. Unfortunately, we show that that the satisfiability problem for this class is no longer polynomial, but CoNP-hard. Furthermore, we devise a PSPACE algorithm to solve this satisfiability problem.