The Complexity of Entailment Problems over Conditional Equality Constraints ?

Equality constraints (a.k.a. unification constraints) have widespread use in static program analysis, most notably in static polymorphic type systems. Conditional equality constraints extend equality constraints with a weak form of subtyping to allow more accurate analyses and more expressive type systems. In this paper, we present a complete complexity characterization of the various entailment problems over conditional equality constraints. In particular, as the main result of the paper, we show that restricted entailment (a.k.a. existential entailment) over conditional equality constraints is PTIME-complete. In addition, we study entailment over a natural extension of conditional equality constraints to provide a boundary between tractable constraint classes and intractable ones w.r.t. entailment.