Graph Path Orderings

Nachum Dershowitz (1) , Jean-Pierre Jouannaud (2, 3)

1 TAU-CS - School of Computer Science
2 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
3 DEDUCTEAM - Deduction modulo, interopérabilité et démonstration automatique

We define well-founded rewrite orderings on graphs and show that they can be used to show termination of a set of graph rewrite rules by verifying all their cyclic extensions. We then introduce the graph path ordering inspired by the recursive path ordering on terms and show that it is a well-founded rewrite ordering on graphs for which checking termination of a finite set of graph rewrite rules is decidable. Our ordering applies to arbitrary finite, directed, labeled, ordered multigraphs, hence provides a building block for rewriting with graphs, which should impact the many areas in which computations take place on graphs.

Domains: Logic in Computer Science [cs.LO]

Nachum Dershowitz, Jean-Pierre Jouannaud. Graph Path Orderings. 22nd International Conference on Logic for Programming, Artificial Intelligence and Reasoning, Nov 2018, Awassa, Ethiopia. pp.1-18. ⟨hal-01903086⟩