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- W3116982904 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." @default.
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- W3116982904 date "2021-01-01" @default.
- W3116982904 modified "2023-09-24" @default.
- W3116982904 title "Deep Weisfeiler Leman" @default.
- W3116982904 doi "https://doi.org/10.1137/1.9781611976465.154" @default.
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