Compositional Propositional Proofs

Abstract

Many hard-combinatorial problems have only be solved by SAT solvers in a massively parallel setting. This reduces the trust one has in the final result as errors might occur during parallel SAT solving or during partitioning of the original problem. We present a new framework to produce clausal proofs for cube-and-conquer, arguably the most effective parallel SAT solving paradigm for hard-combinatorial problems. The framework also provides an elegant approach to parallelize the validation of clausal proofs efficiently, both in terms of run time and memory usage. We evaluate the presented approach on some hard-combinatorial problems and validate constructed clausal proofs in parallel.

Efficient Certified RAT Verification

“…In order to make proof checking feasible in reasonable time, one can check the proof in parallel. This can be achieved by partitioning a proof and verifying each part independently [7]. Let P be a proof of unsatisfiability for a CNF formula F 0 .…”

Condorcet's Principle and the Preference Reversal Paradox

“…It would be desirable to obtain a proof of this claim. While many solvers are able to produce an unsatisfiability proof in a computer-readable format, these proofs can be very big (a recent result in Ramsey theory required 200 TB [19]) and uninsightful. Following Brandt and Geist [7], we use a technique that is sometimes able to produce short and human-readable proofs.…”

Unsatisfiability Proofs for Parallel SAT Solver Portfolios with Clause Sharing and Inprocessing

“…In particular, one can construct certificates from it. For parallel SAT solvers based on the instance decomposition approach, formal models and proof formats exist such as [21,40], and also formalisms that model some portfolios with arbritrary clause sharing but limited formula simplifications [20,34]. However, they do not include the setting by Plingeling.…”