skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


This content will become publicly available on June 1, 2026

Title: Producing Proofs of Unsatisfiability with Distributed Clause-Sharing SAT Solvers
Distributed clause-sharing SAT solvers can solve challenging problems hundreds of times faster than sequential SAT solvers by sharing derived information among multiple sequential solvers. Unlike sequential solvers, however, distributed solvers have not been able to produce proofs of unsatisfiability in a scalable manner, which limits their use in critical applications. In this work, we present a method to produce unsatisfiability proofs for distributed SAT solvers by combining the partial proofs produced by each sequential solver into a single, linear proof. We first describe a simple sequential algorithm and then present a fully distributed algorithm for proof composition, which is substantially more scalable and general than prior works. Our empirical evaluation with over 1500 solver threads shows that our distributed approach allows proof composition and checking within around 3x its own (highly competitive) solving time.  more » « less
Award ID(s):
2415773
PAR ID:
10629074
Author(s) / Creator(s):
; ; ; ;
Publisher / Repository:
Springer
Date Published:
Journal Name:
Journal of Automated Reasoning
Volume:
69
Issue:
2
ISSN:
0168-7433
Subject(s) / Keyword(s):
SAT solving Proofs Distributed computing Cloud computing HPC
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Fisman, D.; Rosu, G. (Ed.)
    When augmented with a Pseudo-Boolean (PB) solver, a Boolean satisfiability (SAT) solver can apply apply powerful reasoning methods to determine when a set of parity or cardinality constraints, extracted from the clauses of the input formula, has no solution. By converting the intermediate constraints generated by the PB solver into ordered binary decision diagrams (BDDs), a proof-generating, BDD-based SAT solver can then produce a clausal proof that the input formula is unsatisfiable. Working together, the two solvers can generate proofs of unsatisfiability for problems that are intractable for other proof-generating SAT solvers. The PB solver can, at times, detect that the proof can exploit modular arithmetic to give smaller BDD representations and therefore shorter proofs. 
    more » « less
  2. Sankaranarayanan, S.; Sharygina, N. (Ed.)
    Modern SAT solvers produce proofs of unsatisfiability to justify the correctness of their results. These proofs, which are usually represented in the well-known DRAT format, can often become huge, requiring multiple gigabytes of disk storage. We present a technique for semantic proof compression that selects a subset of important clauses from a proof and stores them as a so-called proof skeleton. This proof skeleton can later be used to efficiently reconstruct a full proof by exploiting parallelism. We implemented our approach on top of the award-winning SAT solver CaDiCaL and the proof checker DRAT-trim. In an experimental evaluation, we demonstrate that we can compress proofs into skeletons that are 100 to 5,000 times smaller than the original proofs. For almost all problems, proof reconstruction using a skeleton improves the solving time on a single core, and is around five times faster when using 24 cores. 
    more » « less
  3. Groote, J. F.; Larsen, K. G. (Ed.)
    In 2006, Biere, Jussila, and Sinz made the key observation that the underlying logic behind algorithms for constructing Reduced, Ordered Binary Decision Diagrams (BDDs) can be encoded as steps in a proof in the extended resolution logical framework. Through this, a BDD-based Boolean satisfiability (SAT) solver can generate a checkable proof of unsatisfiability. Such proofs indicate that the formula is truly unsatisfiable without requiring the user to trust the BDD package or the SAT solver built on top of it. We extend their work to enable arbitrary existential quantification of the formula variables, a critical capability for BDD-based SAT solvers. We demonstrate the utility of this approach by applying a prototype solver to obtain polynomially sized proofs on benchmarks for the mutilated chessboard and pigeonhole problems—ones that are very challenging for search-based SAT solvers. 
    more » « less
  4. Blanchette, Jasmin; Kovacs, Laura; Pattinson, Dirk (Ed.)
    The propagation redundant (PR) proof system generalizes the resolution and resolution asymmetric tautology proof systems used by conflict-driven clause learning (CDCL) solvers. PR allows short proofs of unsatisfiability for some problems that are difficult for CDCL solvers. Previous attempts to automate PR clause learning used hand-crafted heuristics that work well on some highly-structured problems. For example, the solver SaDiCaL incorporates PR clause learning into the CDCL loop, but it cannot compete with modern CDCL solvers due to its fragile heuristics. We present prExtract, a preprocessing technique that learns short PR clauses. Adding these clauses to a formula reduces the search space that the solver must explore. By performing PR clause learning as a preprocessing stage, PR clauses can be found efficiently without sacrificing the robustness of modern CDCL solvers. On a large portion of SAT competition benchmarks we found that preprocessing with prExtract improves solver performance. In addition, there were several satisfiable and unsatisfiable formulas that could only be solved after preprocessing with prExtract. prExtract supports proof logging, giving a high level of confidence in the results. 
    more » « less
  5. In 2006, Biere, Jussila, and Sinz made the key observation that the underlying logic behind algorithms for constructing Reduced, Ordered Binary Decision Diagrams (BDDs) can be encoded as steps in a proof in the extended resolution logical framework. Through this, a BDD-based Boolean satisfiability (SAT) solver can generate a checkable proof of unsatisfiability. Such a proof indicates that the formula is truly unsatisfiable without requiring the user to trust the BDD package or the SAT solver built on top of it. We extend their work to enable arbitrary existential quantification of the formula variables, a critical capability for BDD-based SAT solvers. We demonstrate the utility of this approach by applying a BDD-based solver, implemented by extending an existing BDD package, to several challenging Boolean satisfiability problems. Our results demonstrate scaling for parity formulas as well as the Urquhart, mutilated chessboard, and pigeonhole problems far beyond that of other proof-generating SAT solvers. 
    more » « less