Universit a Di Pisa (cyclic) Term Graph Rewriting Is Adequate for Rational Parallel Term Rewriting (cyclic) Term Graph Rewriting Is Adequate for Rational Parallel Term Rewriting ?

Acyclic Term Graphs are able to represent terms with sharing , and the relationship between Term Graph Rewriting (TGR) and Term Rewrtiting (TR) is now well understood BvEG + 87, HP91]. During the last years, some researchers considered the extension of TGR to possibly cyclic term graphs, which can represent possibly innnite, rational terms. In KKSdV94] the authors formalize the classical relationship between TGR and TR as an \adequate mapping" between rewriting systems , and extend it by proving that unraveling is an adequate mapping from cyclic TGR to rational, innnitary term rewriting: In fact, a single graph reduction may correspond to an innnite sequence of term reductions. Using the same notions, we propose a diierent adequacy result, showing that unraveling is an adequate mapping from cyclic TGR to rational parallel term rewriting, where at each reduction innnitely many rules can be applied in parallel. We also argue that our adequacy result is more natural than that proposed in KKSdV94], because the length of the reduction sequences is preserved by unraveling, and collapsing rules are treated in a completely uniform way.