Abstract

We investigate set constraints over set expressions with Tarskian functional and relational operations. Unlike the Herbrand constructor symbols used in recent set constraint formalisms, the meaning of a Tarskian function symbol is interpreted in an arbitrary first order structure. We show that satisfiability of Tarskian set constraints is decidable in nondeterministic doubly exponential time. We also consider various extensions of the basic language and show that: satisfiability of Tarskian set constraints with recursion (µ-sets) is undecidable but satisfiability for Tarskian set constraints with µ-sets but without function symbols is linear time equivalent to satisfiability in the propositional µ-calculus and is therefore decidable in deterministic exponential time.

Citations