A survey of SAT solver

Gong, Weiwei; Zhang, Xu

doi:10.1063/1.4981999

Cited by 18 publications

(11 citation statements)

References 44 publications

(43 reference statements)

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“…Finally, we note that the technique used here is related to methods to solve logical puzzles [14]. On the other hand, SAT solvers [1,6,8] provide valuations of the variables such that the given formula evaluates to true, if it is possible. The SAT problem is one of the most known NP-complete problems.…”

Section: Discussionmentioning

confidence: 99%

Optimal Boolean Programming with Graphs

2019

APH

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In this paper, we solve some special types of linear and non-linear Boolean programming problems. We present a method for transforming the used linear 0-1 inequalities into a weighted directed graph. Allowing equalities our conditions are nonlinear, but the transformation to weighted directed graphs works also in these cases. In graph representations, the "critical edges" are used to represent the non-linear conditions. Basic, modified and extended Boolean programming problems are investigated. Linear goal-functions are used in optimization. The presented algorithm, similarly as algorithms for knapsack-problems, gives a relatively good solution, moreover, the algorithm extended by the backtrack graph-search strategy, guarantees optimal solutions for the considered problems.

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Section: Discussionmentioning

confidence: 99%

Optimal Boolean Programming with Graphs

2019

APH

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“…Traveling Salesman [92] Traveling Salesman [93] Multiple Traveling Salesman [94] Bottleneck Traveling Salesman [95] Cutting Stock [96] Cutting Stock [97] 2D Cutting [98] Packing [99] Packing [100] 2D Packing [101] Bin Packing [102] Knapsack [103] Knapsack [104] Subset Sum [105] Unbounded Knapsack [105] Bounded Knapsack [106] Multiple Knapsack [107] Quadratic Knapsack [108] Scheduling [109] Scheduling [110] Production Scheduling [111] Workforce Scheduling [112] Job-Shop Scheduling [113] Precedence Constrained Scheduling [114] Educational Timetabling [115] Educational Timetabling [116] Facility Location [117] Assignment [118] Quadratic Assignment [119] Spanning Tree [120] Maximum Leaf Spanning Tree [121] Degree Constrained Spanning Tree [122] Minimum Spanning Tree [123] Boolean Satisfiability [124] Boolean Satisfiability [125] Covering [126] Minimum Vertex Cover [127] Set Cover [128] Exact Cover [129] Minimum Edge Cover [130] Vehicle Routing [131] Vehicle Routing…”

Section: Type Problemmentioning

confidence: 99%

A Systematic Review of Hyper-Heuristics on Combinatorial Optimization Problems

et al. 2020

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Hyper-heuristics aim at interchanging different solvers while solving a problem. The idea is to determine the best approach for solving a problem at its current state. This way, every time we make a move it gets us closer to a solution. The problem changes; so does its state. As a consequence, for the next move, a different solver may be invoked. Hyper-heuristics have been around for almost 20 years. However, combinatorial optimization problems date from way back. Thus, it is paramount to determine whether the efforts revolving around hyper-heuristic research have been targeted at the problems of the highest interest for the combinatorial optimization community. In this work, we tackle such an endeavor. We begin by determining the most relevant combinatorial optimization problems, and then we analyze them in the context of hyper-heuristics. The idea is to verify whether they remain as relevant when considering exclusively works related to hyper-heuristics. We find that some of the most relevant problem domains have also been popular for hyper-heuristics research. Alas, others have not and few efforts have been directed towards solving them. We identify the following problem domains, which may help in furthering the impact of hyper-heuristics: Shortest Path, Set Cover, Longest Path, and Minimum Spanning Tree. We believe that focusing research on ways for solving them may lead to an increase in the relevance and impact that hyperheuristics have on combinatorial optimization problems.

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“…Most modern complete SAT solvers are based on the the Conflict-Driven Clause Learning (CDCL) algorithm (Marques-Silva and Sakallah 1999), an evolution of the backtracking Davis-Putnam-Logemann-Loveland (DPLL) algorithm (Davis and Putnam 1960;Davis, Logemann, and Loveland 1962). The main techniques used in CDCL solvers include clause-based learning of conflicts, random restarts, heuristic variable selection, and effective constraintpropagation data structures (Gong and Zhou 2017). Examples of highly efficient complete SAT solvers include Min-iSat (Eén and Sörensson 2003), BerkMin (Goldberg and Novikov 2007), PicoSAT (Biere 2008), Lingeling (Biere 2010), Glusose (Audemard and Simon 2014) and MapleSAT (Liang 2018).…”

Section: Introductionmentioning

confidence: 99%

“…During the main loop, GSAT repeatedly checks the current assignments neighbors and selects a new assignment to maximize the number of satisfied clauses. In contrast, WSAT randomly selects a variable in an unsatisfied clause and inverts its value (Gong and Zhou 2017). On top of these basic algorithms, several heuristics for variable selection have been proposed, such as NSAT (McAllester, Selman, and Kautz 1997), Sparrow (Balint and Fröhlich 2010), and ProbSAT (Balint and Schöning 2012).…”

Section: Introductionmentioning

confidence: 99%

FourierSAT: A Fourier Expansion-Based Algebraic Framework for Solving Hybrid Boolean Constraints

Kyrillidis

Shrivastava

Vardi

et al. 2020

AAAI

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The Boolean SATisfiability problem (SAT) is of central importance in computer science. Although SAT is known to be NP-complete, progress on the engineering side—especially that of Conflict-Driven Clause Learning (CDCL) and Local Search SAT solvers—has been remarkable. Yet, while SAT solvers, aimed at solving industrial-scale benchmarks in Conjunctive Normal Form (CNF), have become quite mature, SAT solvers that are effective on other types of constraints (e.g., cardinality constraints and XORs) are less well-studied; a general approach to handling non-CNF constraints is still lacking. In addition, previous work indicated that for specific classes of benchmarks, the running time of extant SAT solvers depends heavily on properties of the formula and details of encoding, instead of the scale of the benchmarks, which adds uncertainty to expectations of running time.To address the issues above, we design FourierSAT, an incomplete SAT solver based on Fourier analysis of Boolean functions, a technique to represent Boolean functions by multilinear polynomials. By such a reduction to continuous optimization, we propose an algebraic framework for solving systems consisting of different types of constraints. The idea is to leverage gradient information to guide the search process in the direction of local improvements. Empirical results demonstrate that FourierSAT is more robust than other solvers on certain classes of benchmarks.

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A survey of SAT solver

Cited by 18 publications

References 44 publications

Optimal Boolean Programming with Graphs

Optimal Boolean Programming with Graphs

A Systematic Review of Hyper-Heuristics on Combinatorial Optimization Problems

FourierSAT: A Fourier Expansion-Based Algebraic Framework for Solving Hybrid Boolean Constraints

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