QELL: QBF Reasoning with Extended Clause Learning and Levelized SAT Solving

2015 ◽  
pp. 343-359 ◽  
Author(s):  
Kuan-Hua Tu ◽  
Tzu-Chien Hsu ◽  
Jie-Hong R. Jiang
Keyword(s):  
Sat Solving ◽  
Clause Learning

scholarly journals On Division Versus Saturation in Pseudo-Boolean Solving

2019 ◽  
Author(s):  
Stephan Gocht ◽  
Jakob Nordström ◽  
Amir Yehudayoff
Keyword(s):  
Linear Programming ◽  
Cutting Planes ◽  
The Other ◽  
Sat Solving ◽  
Linear Combinations ◽  
Division Rule ◽  
Clause Learning

The conflict-driven clause learning (CDCL) paradigm has revolutionized SAT solving over the last two decades. Extending this approach to pseudo-Boolean (PB) solvers doing 0-1 linear programming holds the promise of further exponential improvements in theory, but intriguingly such gains have not materialized in practice. Also intriguingly, most PB extensions of CDCL use not the division rule in cutting planes as defined in [Cook et al., '87] but instead the so-called saturation rule. To the best of our knowledge, there has been no study comparing the strengths of division and saturation in the context of conflict-driven PB learning, when all linear combinations of inequalities are required to cancel variables. We show that PB solvers with division instead of saturation can be exponentially stronger. In the other direction, we prove that simulating a single saturation step can require an exponential number of divisions. We also perform some experiments to see whether these phenomena can be observed in actual solvers. Our conclusion is that a careful combination of division and saturation seems to be crucial to harness more of the power of cutting planes.

Chapter 3. Complete Algorithms

2021 ◽  
Author(s):  
Adnan Darwiche ◽  
Knot Pipatsrisawat
Keyword(s):  
Real World ◽  
Theoretical Perspective ◽  
Point Of View ◽  
Sat Solving ◽  
Practical Point ◽  
Sat Solvers ◽  
Proof Systems ◽  
Real World Applications ◽  
Clause Learning

Complete SAT algorithms form an important part of the SAT literature. From a theoretical perspective, complete algorithms can be used as tools for studying the complexities of different proof systems. From a practical point of view, these algorithms form the basis for tackling SAT problems arising from real-world applications. The practicality of modern, complete SAT solvers undoubtedly contributes to the growing interest in the class of complete SAT algorithms. We review these algorithms in this chapter, including Davis-Putnum resolution, Stalmarck’s algorithm, symbolic SAT solving, the DPLL algorithm, and modern clause-learning SAT solvers. We also discuss the issue of certifying the answers of modern complete SAT solvers.

Improving SAT Solving Using Monte Carlo Tree Search-Based Clause Learning

2019 ◽  
pp. 107-133
Author(s):  
Oliver Keszocze ◽  
Kenneth Schmitz ◽  
Jens Schloeter ◽  
Rolf Drechsler
Keyword(s):  
Monte Carlo ◽  
Tree Search ◽  
Sat Solving ◽  
Monte Carlo Tree Search ◽  
Clause Learning

scholarly journals Guiding CDCL SAT Search via Random Exploration amid Conflict Depression

2020 ◽  
Vol 34 (02) ◽  
pp. 1428-1435
Author(s):  
Md Solimul Chowdhury ◽  
Martin Müller ◽  
Jia You
Keyword(s):  
Variable Selection ◽  
State Of The Art ◽  
Fast Rate ◽  
Empirical Evaluation ◽  
Sat Solving ◽  
Sat Solvers ◽  
Exploration Strategy ◽  
Clause Learning ◽  
Strong Performance ◽  
Performance Gains

The efficiency of Conflict Driven Clause Learning (CDCL) SAT solving depends crucially on finding conflicts at a fast rate. State-of-the-art CDCL branching heuristics such as VSIDS, CHB and LRB conform to this goal. We take a closer look at the way in which conflicts are generated over the course of a CDCL SAT search. Our study of the VSIDS branching heuristic shows that conflicts are typically generated in short bursts, followed by what we call a conflict depression phase in which the search fails to generate any conflicts in a span of decisions. The lack of conflict indicates that the variables that are currently ranked highest by the branching heuristic fail to generate conflicts. Based on this analysis, we propose an exploration strategy, called expSAT, which randomly samples variable selection sequences in order to learn an updated heuristic from the generated conflicts. The goal is to escape from conflict depressions expeditiously. The branching heuristic deployed in expSAT combines these updates with the standard VSIDS activity scores. An extensive empirical evaluation with four state-of-the-art CDCL SAT solvers demonstrates good-to-strong performance gains with the expSAT approach.

scholarly journals Duplicates of conflict clauses in CDCL derivation and their usage to invert some cryptographic functions

2019 ◽  
pp. 54-66
Author(s):  
В.С. Кондратьев ◽  
А.А. Семенов ◽  
О.С. Заикин
Keyword(s):  
Hash Functions ◽  
Boolean Satisfiability ◽  
Experimental Results ◽  
Sat Solving ◽  
New Approach ◽  
Sat Solvers ◽  
Satisfiability Problems ◽  
Clause Learning ◽  
Sat Solver ◽  
Cryptographic Hash Functions

Изучен феномен повторного порождения конфликтных ограничений SAT-решателями в процессе работы с трудными экземплярами задачи о булевой выполнимости. Данный феномен является следствием применения эвристических механизмов чистки конфликтных баз, которые реализованы во всех современных SAT-решателях, основанных на алгоритме CDCL (Conflict Driven Clause Learning). Описана новая техника, которая позволяет отслеживать повторно порождаемые дизъюнкты и запрещать их последующее удаление. На базе предложенных технических решений построен новый многопоточный SAT-решатель (SAT, SATisfiability), который на ряде SAT-задач, кодирующих обращение криптографических хеш-функций, существенно превзошел по эффективности многопоточные решатели, занимавшие в последние годы высокие места на специализированных соревнованиях. A phenomenon of conflict clauses generated repeatedly by SAT solvers is studied. Such clauses may appear during solving hard Boolean satisfiability problems (SAT). This phenomenon is caused by the fact that the modern SAT solvers are based on the CDCL algorithm that generates conflict clauses. A database of such clauses is periodically and partially cleaned. A new approach for practical SAT solving is proposed. According to this approach, the repeatedly generated conflict clauses are tracked, whereas their further generation is prohibited. Based on this approach, a multithreaded SAT solver was developed. This solver was compared with the best multithreaded SAT solvers awarded during the last SAT competitions. According to the experimental results, the developed solver greatly outperforms its competitors on several SAT instances encoding the inversion of some cryptographic hash functions.

scholarly journals A Verified SAT Solver Framework with Learn, Forget, Restart, and Incrementality

2017 ◽  
Author(s):  
Jasmin Christian Blanchette ◽  
Mathias Fleury ◽  
Christoph Weidenbach
Keyword(s):  
Proof Assistant ◽  
Sat Solving ◽  
Formal Framework ◽  
Clause Learning ◽  
Sat Solver ◽  
A Chain

We developed a formal framework for SAT solving using the Isabelle/HOL proof assistant. Through a chain of refinements, an abstract CDCL (conflict-driven clause learning) calculus is connected to a SAT solver that always terminates with correct answers. The framework offers a convenient way to prove theorems about the SAT solver and experiment with variants of the calculus. Compared with earlier verifications, the main novelties are the inclusion of the CDCL rules for forget, restart, and incremental solving and the use of refinement.

Chapter 7. Proof Complexity and SAT Solving

2021 ◽  
Author(s):  
Sam Buss ◽  
Jakob Nordström
Keyword(s):  
Linear Algebra ◽  
Cutting Planes ◽  
Proof Complexity ◽  
Sat Solving ◽  
Proof Systems ◽  
Frege Systems ◽  
Ample Supply ◽  
Clause Learning ◽  
Algebraic Approaches ◽  
Polynomial Calculus

This chapter gives an overview of proof complexity and connections to SAT solving, focusing on proof systems such as resolution, Nullstellensatz, polynomial calculus, and cutting planes (corresponding to conflict-driven clause learning, algebraic approaches using linear algebra or Gröbner bases, and pseudo-Boolean solving, respectively). There is also a discussion of extended resolution (which is closely related to DRAT proof logging) and Frege and extended Frege systems more generally. An ample supply of references for further reading is provided, including for some topics omitted in this chapter.

scholarly journals Practical Aspects of SAT Solving

10.29007/hnks ◽  
2018 ◽  
Author(s):  
Armin Biere
Keyword(s):  
Automated Reasoning ◽  
Sat Solving ◽  
Current Trends ◽  
Recent Developments ◽  
Clause Learning ◽  
Sat Solver

SAT solving techniques are used in many automated reasoning engines. This talk gives an overview on recent developments in practical aspects of SAT solver development. Beside improvements of the basic conflict driven clause learning (CDCL) algorithm, we also discuss improving and integrating advanced preprocessing techniques as inprocessing during search. The talk concludes with a brief overview on current trends in parallelizing SAT.

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