eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-08-18
37:1
37:16
10.4230/LIPIcs.MFCS.2021.37
article
On the Relative Power of Linear Algebraic Approximations of Graph Isomorphism
Dawar, Anuj
1
https://orcid.org/0000-0003-4014-8248
Vagnozzi, Danny
1
Department of Computer Science and Technology, University of Cambridge, UK
We compare the capabilities of two approaches to approximating graph isomorphism using linear algebraic methods: the invertible map tests (introduced by Dawar and Holm) and proof systems with algebraic rules, namely polynomial calculus, monomial calculus and Nullstellensatz calculus. In the case of fields of characteristic zero, these variants are all essentially equivalent to the Weisfeiler-Leman algorithms. In positive characteristic we show that the distinguishing power of the monomial calculus is no greater than the invertible map method by simulating the former in a fixed-point logic with solvability operators. In turn, we show that the distinctions made by this logic can be implemented in the Nullstellensatz calculus.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol202-mfcs2021/LIPIcs.MFCS.2021.37/LIPIcs.MFCS.2021.37.pdf
Graph isomorphism
proof complexity
invertible map tests