MAX - PLANCK - INSTITUT FÜR INFORMATIK Set Constraints are the Monadic Class

We investigate the relationship between set constraints and the monadic class of first-order formulas and show that set constraints are essentially equivalent to the monadic class. From this equivalence we can infer that the satisfiability problem for set constraints is complete for NEXPTIME. More precisely, we prove that this problem has a lower bound of NTIME(cn/ logn). The relationship between set constraints and the monadic class also gives us decidability and complexity results for certain practically useful extensions of set constraints, in particular “negative projections” and subterm equality tests.