Proceedings of SAT Competition 2018 : Solver and Benchmark Descriptions

Non peer reviewe

Can QQ-Learning with Graph Networks Learn a Generalizable Branching Heuristic for a SAT Solver?

We present Graph-$Q$-SAT, a branching heuristic for a Boolean SAT solver trained with value-based reinforcement learning (RL) using Graph Neural Networks for function approximation. Solvers using Graph-$Q$-SAT are complete SAT solvers that either provide a satisfying assignment or proof of unsatisfiability, which is required for many SAT applications. The branching heuristics commonly used in SAT solvers make poor decisions during their warm-up period, whereas Graph-$Q$-SAT is trained to examine the structure of the particular problem instance to make better decisions early in the search. Training Graph-$Q$-SAT is data efficient and does not require elaborate dataset preparation or feature engineering. We train Graph-$Q$-SAT using RL interfacing with MiniSat solver and show that Graph-$Q$-SAT can reduce the number of iterations required to solve SAT problems by 2-3X. Furthermore, it generalizes to unsatisfiable SAT instances, as well as to problems with 5X more variables than it was trained on. We show that for larger problems, reductions in the number of iterations lead to wall clock time reductions, the ultimate goal when designing heuristics. We also show positive zero-shot transfer behavior when testing Graph-$Q$-SAT on a task family different from that used for training. While more work is needed to apply Graph-$Q$-SAT to reduce wall clock time in modern SAT solving settings, it is a compelling proof-of-concept showing that RL equipped with Graph Neural Networks can learn a generalizable branching heuristic for SAT search.Comment: Camera-ready for NeurIPS 202

Proceedings of SAT Competition 2021 : Solver and Benchmark Descriptions

Non peer reviewe

Machine Learning for SAT: Restricted Heuristics and New Graph Representations

Boolean satisfiability (SAT) is a fundamental NP-complete problem with many applications, including automated planning and scheduling. To solve large instances, SAT solvers have to rely on heuristics, e.g., choosing a branching variable in DPLL and CDCL solvers. Such heuristics can be improved with machine learning (ML) models; they can reduce the number of steps but usually hinder the running time because useful models are relatively large and slow. We suggest the strategy of making a few initial steps with a trained ML model and then releasing control to classical heuristics; this simplifies cold start for SAT solving and can decrease both the number of steps and overall runtime, but requires a separate decision of when to release control to the solver. Moreover, we introduce a modification of Graph-Q-SAT tailored to SAT problems converted from other domains, e.g., open shop scheduling problems. We validate the feasibility of our approach with random and industrial SAT problems

Breaking Instance-Independent Symmetries In Exact Graph Coloring

Code optimization and high level synthesis can be posed as constraint satisfaction and optimization problems, such as graph coloring used in register allocation. Graph coloring is also used to model more traditional CSPs relevant to AI, such as planning, time-tabling and scheduling. Provably optimal solutions may be desirable for commercial and defense applications. Additionally, for applications such as register allocation and code optimization, naturally-occurring instances of graph coloring are often small and can be solved optimally. A recent wave of improvements in algorithms for Boolean satisfiability (SAT) and 0-1 Integer Linear Programming (ILP) suggests generic problem-reduction methods, rather than problem-specific heuristics, because (1) heuristics may be upset by new constraints, (2) heuristics tend to ignore structure, and (3) many relevant problems are provably inapproximable. Problem reductions often lead to highly symmetric SAT instances, and symmetries are known to slow down SAT solvers. In this work, we compare several avenues for symmetry breaking, in particular when certain kinds of symmetry are present in all generated instances. Our focus on reducing CSPs to SAT allows us to leverage recent dramatic improvement in SAT solvers and automatically benefit from future progress. We can use a variety of black-box SAT solvers without modifying their source code because our symmetry-breaking techniques are static, i.e., we detect symmetries and add symmetry breaking predicates (SBPs) during pre-processing. An important result of our work is that among the types of instance-independent SBPs we studied and their combinations, the simplest and least complete constructions are the most effective. Our experiments also clearly indicate that instance-independent symmetries should mostly be processed together with instance-specific symmetries rather than at the specification level, contrary to what has been suggested in the literature

Decision Heuristics in a Constraint-based Product Configurator

This paper presents an evaluation of decision heuristics of solvers of the Boolean satisfiability problem (SAT) in the context of constraint-based product configuration. In product configuration, variable assignments are searched in real-time, based on interactively formulated user requirements. Operating on user’s successive input poses new requirements, such as low-latency interactivity as well as deterministic and minimal implicit product changes. This work presents a performance evaluation of several heuristics from the SAT literature along with new variants that address the special real-time requirements of incremental product configuration. Our results show that the execution time on an industrial benchmark can be significantly improved with our new heuristic