Unit propagation with stable watches

Unit propagation is the hottest path in CDCL SAT solvers, therefore the related data-structures, algorithms and implementation details are well studied and highly optimized. State-of-the-art implementations are based on reduced occurrence tracking with two watched literals per clause and one blocking literal per watcher in order to further reduce the number of clause accesses. In this paper, we show that using runtime statistics for watched literal selection can improve the performance of state-of-the-art SAT solvers. We present a method for efficiently keeping track of spans during which literals are satisfied and using this statistic to improve watcher selection. An implementation of our method in the SAT solver CaDiCaL can solve more instances of the SAT Competition 2019 and 2020 benchmark sets and is specifically strong on satisfiable cryptographic instances

GPU Parallelism for SAT Solving Heuristics

Modern SAT solvers employ a number of smart techniques and strategies to achieve maximum efficiency in solving the Boolean Satisfiability problem. Among all components of a solver, the branching heuristics plays a crucial role in affecting the performance of the entire solver. Traditionally, the main branching heuristics that have appeared in the literature have been classified as look-back heuristics or look-ahead heuristics. As SAT technology has evolved, the former have become more and more preferable, for their demand for less computational effort. Graphics Processor Units (GPUs) are massively parallel devices that have spread enormously over the past few decades and offer great computing power at a relatively low cost. We describe how to exploit such computational power to efficiently implement look-ahead heuristics. Our aim is to “rehabilitate” these heuristics, by showing their effectiveness in the contest of a parallel SAT solver

Inference-Guiding for Intelligent Agents

In many applications of intelligent agents, initially given facts are not sufficient to reach a decision, and more data are needed. In that case. Inference-guiding is needed to identify the missing information and lead inference to a conclusion. This paper presents a new inferenceguiding strategy that selects the key pieces of missing information in such a way that the total cost of acquiring additional information for reaching a conclusion is the lowest. The computational experiments show that the new strategy is more effective and economical than the inference-guiding strategies currently available for the intelligent systems

Learning Heuristics for Quantified Boolean Formulas through Deep Reinforcement Learning

We demonstrate how to learn efficient heuristics for automated reasoning algorithms for quantified Boolean formulas through deep reinforcement learning. We focus on a backtracking search algorithm, which can already solve formulas of impressive size - up to hundreds of thousands of variables. The main challenge is to find a representation of these formulas that lends itself to making predictions in a scalable way. For a family of challenging problems, we learned a heuristic that solves significantly more formulas compared to the existing handwritten heuristics