Vijay Ganesh

A machine learning based splitting heuristic for divide-and-conquer solvers

By Saeed Nejati, Ludovic Le Frioux, Vijay Ganesh

2020-12-31

In Proceedings of the 26 th international conference on principles and practice of constraint programming (CP’20)

Abstract

In this paper, we present a machine learning based splitting heuristic for divide-and-conquer parallel Boolean SAT solvers. Splitting heuristics, whether they are look-ahead or look-back, are designed using proxy metrics, which when optimized, approximate the true metric of minimizing solver runtime on sub-formulas resulting from a split. The rationale for such metrics is that they have been empirically shown to be excellent proxies for runtime of solvers, in addition to being cheap to compute in an online fashion. However, the design of traditional splitting methods are often ad-hoc and do not leverage the copious amounts of data that solvers generate. To address the above-mentioned issues, we propose a machine learning based splitting heuristic that leverages the features of input formulas and data generated during the run of a divide-and-conquer (DC) parallel solver. More precisely, we reformulate the splitting problem as a ranking problem and develop two machine learning models for pairwise ranking and computing the minimum ranked variable. Our model can compare variables according to their splitting quality, which is based on a set of features extracted from structural properties of the input formula, as well as dynamic probing statistics, collected during the solver’s run. We derive the true labels through offline collection of runtimes of a parallel DC solver on sample formulas and variables within them. At each splitting point, we generate a predicted ranking (pairwise or minimum rank) of candidate variables and split the formula on the top variable. We implemented our heuristic in the Painless parallel SAT framework and evaluated our solver on a set of cryptographic instances encoding the SHA-1 preimage as well as SAT competition 2018 and 2019 benchmarks. We solve significantly more instances compared to the baseline Painless solver and outperform top divide-and-conquer solvers from recent SAT competitions, such as Treengeling. Furthermore, we are much faster than these top solvers on cryptographic benchmarks.

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Community and LBD-based clause sharing policy for parallel SAT solving

By Vincent Vallade, Ludovic Le Frioux, Souheib Baarir, Julien Sopena, Vijay Ganesh, Fabrice Kordon

2020-06-01

In Proceedings of the 23rd international conference on theory and applications of satisfiability testing (SAT’20)

Abstract

Modern parallel SAT solvers rely heavily on effective clause sharing policies for their performance. The core problem being addressed by these policies can be succinctly stated as “the problem of identifying high-quality learnt clauses” that when shared between the worker nodes of parallel solvers results in improved performance than otherwise. The term “high-quality clauses” is often defined in terms of metrics that solver designers have identified over years of empirical study. Some of the more well-known metrics to identify high-quality clauses for sharing include clause length, literal block distance (LBD), and clause usage in propagation. In this paper, we propose a new metric aimed at identifying high-quality learnt clauses and a concomitant clause-sharing policy based on a combination of LBD and community structure of Boolean formulas. The concept of community structure has been proposed as a possible explanation for the extraordinary performance of SAT solvers in industrial instances. Hence, it is a natural candidate as a basis for a metric to identify high-quality clauses. To be more precise, our metric identifies clauses that have low LBD and low community number as ones that are high-quality for applications such as verification and testing. The community number of a clause C measures the number of different communities of a formula that the variables in C span. We perform extensive empirical analysis of our metric and clause-sharing policy, and show that our method significantly outperforms state-of-the-art techniques on the benchmark from the parallel track of the last four SAT competitions.

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