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Abstract:
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 the nice property that satisfiability can be tested in cubic
time. This is in contrast to 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.
