Faster Certified Symmetry Breaking using Orders with Auxiliary Variables
Paper i 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.
Författare
Markus Anders
RPTU Kaiserslautern-Landau
Bart Bogaerts
KU Leuven
Benjamin Bogø
Köpenhamns universitet
Arthur Gontier
University of Glasgow
Wietze Koops
Lunds universitet
Ciaran McCreesh
University of Glasgow
Magnus Myreen
Göteborgs universitet
Chalmers, Data- och informationsteknik, Formella metoder
Jakob Nordström
Köpenhamns universitet
Andy Oertel
Lunds universitet
Adrian Rebola-Pardo
Technische Universität Wien
Yong Kiam Tan
Nanyang Technological University
Proceedings of the AAAI Conference on Artificial Intelligence
21595399 (ISSN) 23743468 (eISSN)
Vol. 40 17 14140-141489781577359067 (ISBN)
AAAI Conference on Artificial Intelligence
, Singapore,
, Singapore,
De nästa 700 verifierade kompilatorerna
Vetenskapsrådet (VR) (2021-05165), 2022-01-01 -- 2025-12-31.
Ämneskategorier (SSIF 2025)
Datavetenskap (datalogi)
DOI
10.1609/aaai.v40i17.38426