SAT Competition 2020

Froleyks, Nils; Heule, Marijn J. H.; Iser, Markus; Järvisalo, Matti; Suda, Martin

doi:10.1016/j.artint.2021.103572

Cited by 32 publications

(14 citation statements)

References 44 publications

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“…We obtained a relevant, diverse, and well-documented pool of instances by choosing all instances from the SAT Competition 2020 which were solved by Glucose 3.0 between 30 min and 5000 s (≈ 83 min). The upper bound comes from a time limit imposed in the SAT Competition itself, where all solvers are cut off after 5000 s. A more detailed description of all selected instances can be found in S2 Table . We also refer to the proceedings of the SAT Competition 2020 [36,37]. A vigilant reader may notice that we have 53 instances in our pool, whereas our selection criterion applies to 61 instances of the SAT Competition 2020.…”

Section: Methodsmentioning

confidence: 99%

Too much information: why CDCL solvers need to forget learned clauses

Krüger,

Lorenz,

Wörz

2022

Preprint

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Conflict-driven clause learning (CDCL) is a remarkably successful paradigm for solving the satisfiability problem of propositional logic. Instead of a simple depth-first backtracking approach, this kind of solver learns the reason behind occurring conflicts in the form of additional clauses. However, despite the enormous success of CDCL solvers, there is still only a shallow understanding of what influences the performance of these solvers in what way. This paper will demonstrate, quite surprisingly, that clause learning (without being able to get rid of some clauses) can not only improve the runtime but can oftentimes deteriorate it dramatically. By conducting extensive empirical analysis, we find that the runtime distributions of CDCL solvers are multimodal. This multimodality can be seen as a reason for the deterioration phenomenon described above. Simultaneously, it also gives an indication of why clause learning in combination with clause deletion and restarts is virtually the de facto standard of SAT solving in spite of this phenomenon. As a final contribution, we will show that Weibull mixture distributions can accurately describe the multimodal distributions. Thus, adding new clauses to a base instance has an inherent effect of making runtimes long-tailed. This insight provides a theoretical explanation as to why the techniques of restarts and clause deletion are useful in CDCL solvers.

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Section: Methodsmentioning

confidence: 99%

Too much information: why CDCL solvers need to forget learned clauses

Krüger,

Lorenz,

Wörz

2022

Preprint

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“…The malleable environment of this solver is the system which we present here. Other recent works on decentralized SAT solving [15,21] rely on a different parallelization which generates many independent subproblems and tends to be outperformed by parallel portfolios for most practical inputs [11].…”

Section: Scalable Sat Solvingmentioning

confidence: 99%

Decentralized Online Scheduling of Malleable NP-hard Jobs

Sanders

Schreiber

2022

Euro-Par 2022: Parallel Processing

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In this work, we address an online job scheduling problem in a large distributed computing environment. Each job has a priority and a demand of resources, takes an unknown amount of time, and is malleable, i.e., the number of allotted workers can fluctuate during its execution. We subdivide the problem into (a) determining a fair amount of resources for each job and (b) assigning each job to an according number of processing elements. Our approach is fully decentralized, uses lightweight communication, and arranges each job as a binary tree of workers which can grow and shrink as necessary. Using the NP-complete problem of propositional satisfiability (SAT) as a case study, we experimentally show on up to 128 machines (6144 cores) that our approach leads to near-optimal utilization, imposes minimal computational overhead, and performs fair scheduling of incoming jobs within a few milliseconds.

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“…We study how three solvers compare on the full set of 849 hard benchmarks. We consider the number of solved benchmarks and another important metric, the PAR-2 score used in SAT competitions [Balint et al, 2015, Froleyks et al, 2021. Given a solver s and a benchmark b, the PAR-2 score, score (s, b), is the solving time if the solver solves the benchmark (within memory and time limits) and is twice the 1000-second time cap otherwise.…”

Section: Overall Performancementioning

confidence: 99%

DPER: Dynamic Programming for Exist-Random Stochastic SAT

Phan¹,

Vardi²

2022

Preprint

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In Bayesian inference, the maximum a posteriori (MAP) problem combines the most probable explanation (MPE) and marginalization (MAR) problems. The counterpart in propositional logic is the exist-random stochastic satisfiability (ER-SSAT) problem, which combines the satisfiability (SAT) and weighted model counting (WMC) problems. Both MAP and ER-SSAT have the form argmax X Y f (X, Y ), where f is a real-valued function over disjoint sets X and Y of variables. These two optimization problems request a value assignment for the X variables that maximizes the weighted sum of f (X, Y ) over all value assignments for the Y variables. ER-SSAT has been shown to be a promising approach to formally verify fairness in supervised learning. Recently, dynamic programming on graded project-join trees has been proposed to solve weighted projected model counting (WPMC), a related problem that has the form X max Y f (X, Y ). We extend this WPMC framework to exactly solve ER-SSAT and implement a dynamic-programming solver named DPER. Our empirical evaluation indicates that DPER contributes to the portfolio of state-of-the-art ER-SSAT solvers (DC-SSAT and erSSAT) through competitive performance on low-width problem instances.

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SAT Competition 2020

Cited by 32 publications

References 44 publications

Too much information: why CDCL solvers need to forget learned clauses

Too much information: why CDCL solvers need to forget learned clauses

Decentralized Online Scheduling of Malleable NP-hard Jobs

DPER: Dynamic Programming for Exist-Random Stochastic SAT

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