Faster Certified Symmetry Breaking using Orders with Auxiliary Variables
Paper in proceeding, 2026
Symmetry breaking is a crucial technique in modern combinatorial solving, but it is difficult to be sure it is implemented correctly. The most successful approach to deal with bugs is to make solvers certifying, so that they output not just a solution, but also a mathematical proof of correctness in a standard format, which can then be checked by a formally verified checker. This requires justifying symmetry reasoning within the proof, but developing efficient methods for this has remained a long-standing open challenge. A fully general approach was recently proposed by Bogaerts et al. (2023), but it relies on encoding lexicographic orders with big integers, which quickly becomes infeasible for large symmetries. In this work, we develop a method for instead encoding orders with auxiliary variables. We show that this leads to orders-ofmagnitude speed-ups in both theory and practice by running experiments on proof logging and checking for SAT symmetry breaking using the state-of-the-art SATSUMA symmetry breaker and the VERIPB proof checking toolchain.
Author
Markus Anders
RPTU Kaiserslautern-Landau
Bart Bogaerts
KU Leuven
Benjamin Bogø
University of Copenhagen
Arthur Gontier
University of Glasgow
Wietze Koops
Lund University
Ciaran McCreesh
University of Glasgow
Magnus Myreen
Chalmers, Computer Science and Engineering (Chalmers), Formal methods
University of Gothenburg
Jakob Nordström
University of Copenhagen
Andy Oertel
Lund University
Adrian Rebola-Pardo
Vienna University of Technology
Yong Kiam Tan
Nanyang Technological University
Fortieth AAAI Conference on Artificial Intelligence
2374-3468 (ISSN) 2374-3468 (eISSN)
Vol. 40 17
AAAI Conference on Artificial Intelligence
, Singapore,
, Singapore,
The next 700 verified compilers
Swedish Research Council (VR) (2021-05165), 2022-01-01 -- 2025-12-31.
Subject Categories (SSIF 2025)
Computer Sciences
DOI
10.1609/aaai.v40i17.38426