1,700 research outputs found
Community structure in industrial SAT instances
Modern SAT solvers have experienced a remarkable progress on solving industrial instances. It is believed that most of these successful techniques exploit the underlying structure of industrial instances. Recently, there have been some attempts to analyze the structure of industrial SAT instances in terms of complex networks, with the aim of explaining the success of SAT solving techniques, and possibly improving them.
In this paper, we study the community structure, or modularity, of industrial SAT instances. In a graph with clear community structure, or high modularity, we can find a partition of its nodes into communities such that most edges connect variables of the same community. Representing SAT instances as graphs, we show that most application benchmarks are characterized by a high modularity. On the contrary, random SAT instances are closer to the classical Erdös-Rényi random graph model, where no structure can be observed. We also analyze how this structure evolves by the effects of the execution of a CDCL SAT solver, and observe that new clauses learned by the solver during the search contribute to destroy the original structure of the formula. Motivated by this observation, we finally present an application that exploits the community structure to detect relevant learned clauses, and we show that detecting these clauses results in an improvement on the performance of the SAT solver. Empirically, we observe that this improves the performance of several SAT solvers on industrial SAT formulas, especially on satisfiable instances.Peer ReviewedPostprint (published version
A Time Leap Challenge for SAT Solving
We compare the impact of hardware advancement and algorithm advancement for
SAT solving over the last two decades. In particular, we compare 20-year-old
SAT-solvers on new computer hardware with modern SAT-solvers on 20-year-old
hardware. Our findings show that the progress on the algorithmic side has at
least as much impact as the progress on the hardware side.Comment: Authors' version of a paper which is to appear in the proceedings of
CP'202
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
Can -Learning with Graph Networks Learn a Generalizable Branching Heuristic for a SAT Solver?
We present Graph--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--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--SAT is trained to examine the structure of
the particular problem instance to make better decisions early in the search.
Training Graph--SAT is data efficient and does not require elaborate dataset
preparation or feature engineering. We train Graph--SAT using RL interfacing
with MiniSat solver and show that Graph--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--SAT on a task family different from that used for training.
While more work is needed to apply Graph--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
On P-transitive graphs and applications
We introduce a new class of graphs which we call P-transitive graphs, lying
between transitive and 3-transitive graphs. First we show that the analogue of
de Jongh-Sambin Theorem is false for wellfounded P-transitive graphs; then we
show that the mu-calculus fixpoint hierarchy is infinite for P-transitive
graphs. Both results contrast with the case of transitive graphs. We give also
an undecidability result for an enriched mu-calculus on P-transitive graphs.
Finally, we consider a polynomial time reduction from the model checking
problem on arbitrary graphs to the model checking problem on P-transitive
graphs. All these results carry over to 3-transitive graphs.Comment: In Proceedings GandALF 2011, arXiv:1106.081
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