Deep Weisfeiler Leman

Society for Industrial and Applied Mathematics eBooks, pp. 2600–2614

Abstract

We introduce the framework of Deep Weisfeiler Leman algorithms (DeepWL), which allows the design of purely combinatorial graph isomorphism tests that are more powerful than the well-known Weisfeiler-Leman algorithm. We prove that, as an abstract computational model, polynomial-time DeepWL-algorithms have exactly the same expressiveness as the logic Choiceless Polynomial Time (with counting) introduced by Blass, Gurevich, and Shelah (Ann. Pure Appl. Logic., 1999). It is a well-known open question whether the existence of a polynomial-time graph isomorphism test implies the existence of a polynomial-time canonisation algorithm. Our main technical result states that for each class of graphs (satisfying some mild closure condition), if there is a polynomial-time DeepWL isomorphism test, then there is a polynomial-time canonisation algorithm for this class. This implies that there is also a logic capturing polynomial time on this class.

Authors 3

1. Martin Grohe Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Aachen, Germany

2. Pascal Schweitzer

   University of Kaiserslautern

   Affiliation as printed

   TU Kaiserslautern. Supp

   University of Kaiserslautern, Kaiserslautern, Germany

3. Daniel Wiebking Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University

   RWTH Aachen University, Aachen, Germany