Set Constraints with Projections
Set constraints form a constraint system where variables range over the domain of sets of trees. They give a natural formalism for many problems in program analysis. Syntactically, set constraints are conjunctions of inclusions between expressions built over variables, constructors (constants and function symbols from a given signature) and a choice of set operators that defines the specific class of set constraints. In this article, we are interested in the class of set constraints with projections, which is the class with all Boolean operators (union, intersection and complement) and projections that in program analysis directly correspond to type destructors. We prove that the problem of existence of a solution of a system of set constraints with projections is in NEXPTIME, and thus that it is NEXPTIME-complete.
set constraints program analysis algorithms theory computational complexity