Andy Oertel

Hannes Ihalainen, Andy Oertel, Yong Kiam Tan et al.

Building on the progress in Boolean satisfiability (SAT) solving over the last decades, maximum satisfiability (MaxSAT) has become a viable approach for solving NP-hard optimization problems, but ensuring correctness of MaxSAT solvers has remained an important concern. For SAT, this is largely a solved problem thanks to the use of proof logging, meaning that solvers emit machine-verifiable proofs of (un)satisfiability to certify correctness. However, for MaxSAT, proof logging solvers have started being developed only very recently. Moreover, these nascent efforts have only targeted the core solving process, ignoring the preprocessing phase where input problem instances can be substantially reformulated before being passed on to the solver proper. In this work, we demonstrate how pseudo-Boolean proof logging can be used to certify the correctness of a wide range of modern MaxSAT preprocessing techniques. By combining and extending the VeriPB and CakePB tools, we provide formally verified, end-to-end proof checking that the input and preprocessed output MaxSAT problem instances have the same optimal value. An extensive evaluation on applied MaxSAT benchmarks shows that our approach is feasible in practice.

Markus Anders, Bart Bogaerts, Benjamin Bogø et al.

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-of-magnitude 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.