Analysis of Rewriting-Based Systems as First-Order Theories

Computational systems based on a first-order language that can be given a canonical model which captures provability in the corresponding calculus can often be seen as first-order theories S, and computational properties of such systems can be formulated as first-order sentences. that hold in such a canonical model of S. In this setting, standard results regarding the preservation of satisfiability of different classes of first-order sentences yield a number of interesting applications in program analysis. In particular, properties expressed as existentially quantified boolean combinations of atoms (for instance, a set of unification problems) can then be disproved by just finding an arbitrary model of the considered theory plus the negation of such a sentence. We show that rewriting-based systems fit into this approach. Many computational properties (e.g., infeasibility and non-joinability of critical pairs in (conditional) rewriting, non-loopingness, or the secure access to protected pages of a web site) can be investigated in this way. Interestingly, this semantic approach succeeds when specific techniques developed to deal with the aforementioned problems fail.