Paths vs. trees in set-based program analysis

Abstract

Set-based analysis of logic programs provides an accurate method for descriptive type-checking of logic programs. The key idea of this method is to upper approximate the least model of the program by a regular set of trees. In 1991, Fruhwirth, Shapiro, Vardi and Yardeni raised the question whether it can be more efficient to use the domain of sets of paths instead, i.e., to approximate the least model by a regular set of words. We answer the question negatively by showing that type-checking for path-based analysis is as hard as the set-based one, that is DEXPTIME-complete. This result has consequences also in the areas of set constraints, automata theory and model checking.