Approximating Term Rewriting Systems: A Horn Clause Specification and Its Implementation

Characterizing Conclusive Approximations by Logical Formulae

“…In the field of the tree automata completion, an approximation is precised enough as soon as this latter allows us to show the unreachability of a term or a set of terms. In this context, our proposition allows us to find only conclusive approximations, contrary to the ones obtained in [10]. Indeed, our approach is in some sense goal oriented while the one proposed in [10] check the reachability of a term only after having computed an approximation.…”

“…In this context, our proposition allows us to find only conclusive approximations, contrary to the ones obtained in [10]. Indeed, our approach is in some sense goal oriented while the one proposed in [10] check the reachability of a term only after having computed an approximation. 2 The Mona program and thus the formula φ This work is a first step towards a verification technique based on formula solving.…”

“…In [10], the authors encode the tree automata completion by logic programs (Horn clauses). Consequently, they use several results obtained on static analysis of logic programs in order to compute precise approximations in the sense of static analysis.…”

Proving semantic properties as first-order satisfiability

“…Gallagher and Rosendahl use Horn clauses to encode TRSs and then investigate reachability issues [17]. Their approach, however, is quite different from ours.…”

“…Such a semantic description is implicit (and therefore fixed ) in their encoding. Also, we view rewrite rules → r just as atoms for a binary predicate →, whereas they translate each rewrite rule into several Horn clauses which flatten the original terms to simulate pattern matching [17,Section 3]. Furthermore, we do not restrict the attention to TRSs; our method applies to more general rewriting-based systems.…”