Deciding in HFS-Theory via Linear Integer Programming

We give a reduction, in polynomialy bounded time, of the satisfiability problem in the set language MPLS, to an equivalent linear integer programming problem. We show that this provides an algorithm to decide the Set Unification Problem. The procedure performed gives the eventual unifiers of two set terms (i.e. at least a minimal exhaustive collection of unifiers) in “compact form”. The unifiers are given via the solutions of a linear integer system generated by the reduction. We also report further results concerning the construction of models over the atoms of the universe HFSA (the set model conceived here). These predict the number of useful atoms needed to produce a model of formulae involving the negation.