More Like this

1. From Clauses to Klauses

   Reeves, Joseph E; Heule, Marijn; Bryant, Randal E (July 2024, International Conference on Computer Aided Verification (CAV-24))

   Satisfiability (SAT) solvers have been using the same input format for decades: a formula in conjunctive normal form. Cardinality constraints appear frequently in problem descriptions: over 64% of the SAT Competition formulas contain at least one cardinality constraint, while over 17% contain many large cardinality constraints. Allowing general cardinality constraints as input would simplify encodings and enable the solver to handle constraints natively or to encode them using different (and possibly dynamically changing) clausal forms. We modify the modern SAT solver CaDiCaL to handle cardinality constraints natively. Unlike the stronger cardinality reasoning in pseudo-Boolean (PB) or other systems, our incremental approach with cardinality-based propagation requires only moderate changes to a SAT solver, preserves the ability to run important inprocessing techniques, and is easily combined with existing proof-producing and validation tools. Our experimental evaluation on SAT Competition formulas shows our solver configurations with cardinality support consistently outperform other SAT and PB solvers. 

   more » « less
2. Augmenting an electronic Ising machine to effectively solve boolean satisfiability

   https://doi.org/10.1038/s41598-023-49966-6  

   Sharma, Anshujit; Burns, Matthew; Hahn, Andrew; Huang, Michael (December 2023, Scientific Reports)

   Abstract With the slowdown of improvement in conventional von Neumann systems, increasing attention is paid to novel paradigms such as Ising machines. They have very different approach to solving combinatorial optimization problems. Ising machines have shown great potential in solving binary optimization problems like MaxCut. In this paper, we present an analysis of these systems in boolean satisfiability (SAT) problems. We demonstrate that, in the case of 3-SAT, a basic architecture fails to produce meaningful acceleration, largely due to the relentless progress made in conventional SAT solvers. Nevertheless, careful analysis attributes part of the failure to the lack of two important components: cubic interactions and efficient randomization heuristics. To overcome these limitations, we add proper architectural support for cubic interaction on a state-of-the-art Ising machine. More importantly, we propose a novel semantic-aware annealing schedule that makes the search-space navigation much more efficient than existing annealing heuristics. Using numerical simulations, we show that such an “Augmented” Ising Machine for SAT is projected to outperform state-of-the-art software-based, GPU-based and conventional hardware SAT solvers by orders of magnitude. 

   more » « less
3. Benchmarking the Capabilities and Limitations of SAT Solvers in Defeating Obfuscation Schemes

   https://doi.org/10.1109/IOLTS.2018.8474189  

   Roshanisefat, Shervin; Thirumala, Harshith K.; Gaj, Kris; Homayoun, Houman; Sasan, Avesta (July 2018, 2018 IEEE 24th International Symposium on On-Line Testing And Robust System Design (IOLTS))

   In this paper, we investigate the strength of six different SAT solvers in attacking various obfuscation schemes. Our investigation revealed that Glucose and Lingeling SAT solvers are generally suited for attacking small-to-midsize obfuscated circuits, while the MapleGlucose, if the system is not memory bound, is best suited for attacking mid-to-difficult obfuscation methods. Our experimental result indicates that when dealing with extremely large circuits and very difficult oufuscation problems, the SAT solver may be memory bound, and Lingeling, for having the most memory efficient implementation, is the best suited solver for such problems. Additionally, our investigation revealed that SAT solver execution times may vary widely across different SAT solvers. Hence, when testing the hardness of an obfuscation methods, although the increase in difficulty could be verified by one SAT solver, the pace of increase in difficulty is dependent on the choice of a SAT solver. 

   more » « less
4. Producing Proofs of Unsatisfiability with Distributed Clause-Sharing SAT Solvers

   https://doi.org/10.1007/s10817-025-09725-w  

   Michaelson, Dawn; Schreiber, Dominik; Heule, Marijn_J H; Kiesl-Reiter, Benjamin; Whalen, Michael W (June 2025, Journal of Automated Reasoning)

   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
5. SMC: Satisfiability Modulo Convex Programming

   https://doi.org/10.1109/JPROC.2018.2849003  

   Shoukry, Yasser; Nuzzo, Pierluigi; Sangiovanni-Vincentelli, Alberto L.; Seshia, Sanjit A.; Pappas, George J.; Tabuada, Paulo (January 2018, Proceedings of the IEEE)

   The design of cyber-physical systems (CPSs) requires methods and tools that can efficiently reason about the interaction between discrete models, e.g., representing the behaviors of ``cyber'' components, and continuous models of physical processes. Boolean methods such as satisfiability (SAT) solving are successful in tackling large combinatorial search problems for the design and verification of hardware and software components. On the other hand, problems in control, communications, signal processing, and machine learning often rely on convex programming as a powerful solution engine. However, despite their strengths, neither approach would work in isolation for CPSs. In this paper, we present a new satisfiability modulo convex programming (SMC) framework that integrates SAT solving and convex optimization to efficiently reason about Boolean and convex constraints at the same time. We exploit the properties of a class of logic formulas over Boolean and nonlinear real predicates, termed monotone satisfiability modulo convex formulas, whose satisfiability can be checked via a finite number of convex programs. Following the lazy satisfiability modulo theory (SMT) paradigm, we develop a new decision procedure for monotone SMC formulas, which coordinates SAT solving and convex programming to provide a satisfying assignment or determine that the formula is unsatisfiable. A key step in our coordination scheme is the efficient generation of succinct infeasibility proofs for inconsistent constraints that can support conflict-driven learning and accelerate the search. We demonstrate our approach on different CPS design problems, including spacecraft docking mission control, robotic motion planning, and secure state estimation. We show that SMC can handle more complex problem instances than state-of-the-art alternative techniques based on SMT solving and mixed integer convex programming. 

   more » « less