scholarly journals Dolius: A Distributed Parallel SAT Solving Framework

10.29007/hvqt ◽  
2018 ◽  
Author(s):  
Gilles Audemard ◽  
Benoît Hoessen ◽  
Saïd Jabbour ◽  
Cédric Piette
Keyword(s):  
Shared Memory ◽  
State Of The Art ◽  
Divide And Conquer ◽  
Sat Solving ◽  
Sat Solvers ◽  
Sat Solver

Over the years, parallel SAT solving becomes more and more important. However, most of state-of-the-art parallel SAT solvers are portfolio-based ones. They aim at running several times the same solver with different parameters. In this paper, we propose a tool called Dolius, mainly based on the divide and conquer paradigm. In contrast to most current parallel efficient engines, Dolius does not need shared memory, can be distributed, and scales well when a large number of computing units is available. Furthermore, our tool contains an API allowing to plug any SAT solver in a simple way.

scholarly journals Framework for Generating Configurable SAT Solvers

2011 ◽  
Vol 6 (1) ◽  
pp. 50-59
Author(s):  
Bernardo C. Vieira ◽  
Fabrício V. Andrade ◽  
Antônio O. Fernandes
Keyword(s):  
State Of The Art ◽  
The State ◽  
Equivalence Checking ◽  
Decision Heuristics ◽  
Sat Solvers ◽  
The Third ◽  
Sat Solver ◽  
Run Time

The state-of-the-art SAT solvers usually share the same core techniques, for instance: the watched literals structure, conflict clause recording and non-chronological backtracking. Nevertheless, they might differ in the elimination of learnt clauses, as well as in the decision heuristic. This article presents a framework for generating configurable SAT solvers. The proposed framework is composed of the following components: a Base SAT Solver, a Perl Preprocessor, XML files (Solver Description and Heuristics Description files) to describe each heuristic as well as the set of heuristics that the generated solver uses. This solvers may use several techniques and heuristics such as those implemented in BerkMin, and in Equivalence Checking of Dissimilar Circuits, and also in Minisat. In order to demonstrate the effectiveness of the proposed framework, this article also presents three distinct SAT solver instances generated by the framework to address a complex and challenging industry problem: the Combinational Equivalence Checking problem (CEC).The first instance is a SAT solver that uses BerkMin and Dissimilar Circuits core techniques except the learnt clause elimination heuristic that has been adapted from Minisat; the second is another solver that combines BerkMin and Minisat decision heuristics at run-time; and the third is yet another SAT solver that changes the database reducing heuristic at run-time. The experiments demonstrate that the first SAT solver generated is a faster solver than state-of-the-art SAT solver BerkMin for several instances as well as for Minisat in almost every instance.

scholarly journals SAT solving experiments in Vampire

10.29007/5l47 ◽  
2018 ◽  
Author(s):  
Armin Biere ◽  
Ioan Dragan ◽  
Laura Kovács ◽  
Andrei Voronkov
Keyword(s):  
State Of The Art ◽  
Theorem Prover ◽  
Sat Solving ◽  
First Order ◽  
Automated Theorem Prover ◽  
Sat Solver ◽  
Overall Performance

In order to better understand how well a state of the art SAT solver would behave in the framework of a first-order automated theorem prover we have decided to integrate Lingeling, best performing SAT solver, inside Vampire’s AVATAR framework. In this paper we propose two ways of integrating a SAT solver inside of Vampire and evaluate overall performance of this combination. Our experiments show that by using a state of the art SAT solver in Vampire we manage to solve more problems. Surprisingly though, there are cases where combination of the two solvers does not always prove to generate best results.

scholarly journals Towards Improving the Resource Usage of SAT-solvers

10.29007/3vwv ◽  
2018 ◽  
Author(s):  
Norbert Manthey ◽  
Ari Saptawijaya
Keyword(s):  
Data Structures ◽  
Memory Access ◽  
Resource Usage ◽  
Sat Solving ◽  
Sat Solvers ◽  
L2 Cache ◽  
Measurement Results ◽  
Sat Solver ◽  
Cache Analysis ◽  
Runtime Performance

The paper presents our work on cache analysis of SAT-solving. The aim is to study how resources are utilized by a SAT-solver and to use this knowledge to improve the resource usage in SAT-solving. The analysis is performed mainly on our CDCL-based SAT-solver and additionally on MiniSAT and PrecoSAT. The measurement is conducted using sample-based profiling on some industrial benchmark from the SAT-competition 2009. During the measurement the following hardware events are traced: total cycles, stall cycles, L2 cache hits and L2 cache misses. From the measurement results, our runtime and implementation analysis unveil that several improvements on resource usage can be done, i.e. on data structures and memory access. These improvements bring about 60% speedup of runtime performance for our solver.

scholarly journals Tuning Parallel SAT Solvers

10.29007/z3g2 ◽  
2019 ◽  
Author(s):  
Thorsten Ehlers ◽  
Dirk Nowotka
Keyword(s):  
Model Checking ◽  
Database Management ◽  
Bounded Model Checking ◽  
Experimental Results ◽  
Massively Parallel ◽  
Sat Solving ◽  
Sat Solvers ◽  
Sat Solver ◽  
The Impact

In this paper we present new implementation details and benchmarking results for our parallel portfolio solver TopoSAT2. In particular, we discuss ideas and implementation details for the exchange of learned clauses in a massively-parallel SAT solver which is designed to run more that 1, 000 solver threads in parallel. Furthermore, we go back to the roots of portfolio SAT solving, and discuss the impact of diversifying the solver by using different restart- , branching- and clause database management heuristics. We show that these techniques can be used to tune the solver towards different problems. However, in a case study on formulas derived from Bounded Model Checking problems we see the best performance when using a rather simple clause exchange strategy. We show details of these tests and discuss possible explanations for this phenomenon.As computing times on massively-parallel clusters are expensive, we consider it especially interesting to share these kind of experimental results.

scholarly journals Community Structure in Industrial SAT Instances

2019 ◽  
Vol 66 ◽  
pp. 443-472
Author(s):  
Carlos Ansótegui ◽  
Maria Luisa Bonet ◽  
Jesús Giráldez-Cru ◽  
Jordi Levy ◽  
Laurent Simon
Keyword(s):  
Community Structure ◽  
Complex Networks ◽  
Graph Model ◽  
Underlying Structure ◽  
Original Structure ◽  
Sat Solving ◽  
Random Graph Model ◽  
Sat Solvers ◽  
Sat Solver ◽  
Remarkable Progress

Modern SAT solvers have experienced a remarkable progress on solving industrial instances. It is believed that most of these successful techniques exploit the underlying structure of industrial instances. Recently, there have been some attempts to analyze the structure of industrial SAT instances in terms of complex networks, with the aim of explaining the success of SAT solving techniques, and possibly improving them. In this paper, we study the community structure, or modularity, of industrial SAT instances. In a graph with clear community structure, or high modularity, we can find a partition of its nodes into communities such that most edges connect variables of the same community. Representing SAT instances as graphs, we show that most application benchmarks are characterized by a high modularity. On the contrary, random SAT instances are closer to the classical Erdös-Rényi random graph model, where no structure can be observed. We also analyze how this structure evolves by the effects of the execution of a CDCL SAT solver, and observe that new clauses learned by the solver during the search contribute to destroy the original structure of the formula. Motivated by this observation, we finally present an application that exploits the community structure to detect relevant learned clauses, and we show that detecting these clauses results in an improvement on the performance of the SAT solver. Empirically, we observe that this improves the performance of several SAT solvers on industrial SAT formulas, especially on satisfiable instances.

Chapter 12. Automated Configuration and Selection of SAT Solvers

2021 ◽  
Author(s):  
Holger H. Hoos ◽  
Frank Hutter ◽  
Kevin Leyton-Brown
Keyword(s):  
Research And Development ◽  
State Of The Art ◽  
Sat Solving ◽  
Sat Solvers ◽  
Effective Application ◽  
Automated Algorithm ◽  
Fertile Ground ◽  
Algorithm Configuration ◽  
Algorithmic Approaches ◽  
Selection Of

This chapter provides an introduction to the automated configuration and selection of SAT algorithms and gives an overview of the most prominent approaches. Since the early 2000s, these so-called meta-algorithmic approaches have played a major role in advancing the state of the art in SAT solving, giving rise to new ways of using and evaluating SAT solvers. At the same time, SAT has proven to be particularly fertile ground for research and development in the area of automated configuration and selection, and methods developed there have meanwhile achieved impact far beyond SAT, across a broad range of computationally challenging problems. Conceptually more complex approaches that go beyond “pure” algorithm configuration and selection are also discussed, along with some open challenges related to meta-algorithmic approaches, such as automated algorithm configuration and selection, to the tools based on these approaches, and to their effective application.

scholarly journals On speeding up factoring with quantum SAT solvers

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Michele Mosca ◽  
Joao Marcos Vensi Basso ◽  
Sebastian R. Verschoor
Keyword(s):  
Number Field ◽  
Classical Method ◽  
Sat Solving ◽  
Smooth Numbers ◽  
Sat Solvers ◽  
Number Field Sieve ◽  
Main Challenge ◽  
Np Hard Problem ◽  
Sat Solver ◽  
Insight Into

Abstract There have been several efforts to apply quantum SAT solving methods to factor large integers. While these methods may provide insight into quantum SAT solving, to date they have not led to a convincing path to integer factorization that is competitive with the best known classical method, the Number Field Sieve. Many of the techniques tried involved directly encoding multiplication to SAT or an equivalent NP-hard problem and looking for satisfying assignments of the variables representing the prime factors. The main challenge in these cases is that, to compete with the Number Field Sieve, the quantum SAT solver would need to be superpolynomially faster than classical SAT solvers. In this paper the use of SAT solvers is restricted to a smaller task related to factoring: finding smooth numbers, which is an essential step of the Number Field Sieve. We present a SAT circuit that can be given to quantum SAT solvers such as annealers in order to perform this step of factoring. If quantum SAT solvers achieve any asymptotic speedup over classical brute-force search for smooth numbers, then our factoring algorithm is faster than the classical NFS.

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 The Hard Problems Are Almost Everywhere For Random CNF-XOR Formulas

2017 ◽  
Author(s):  
Jeffrey M. Dudek ◽  
Kuldeep S. Meel ◽  
Moshe Y. Vardi
Keyword(s):  
State Of The Art ◽  
Solution Space ◽  
Sat Solvers ◽  
Universal Hashing ◽  
Almost Everywhere ◽  
Wide Range ◽  
Sat Solver ◽  
Hard Problems ◽  
Transition Location ◽  
Cnf Formulas

Recent universal-hashing based approaches to sampling and counting crucially depend on the runtime performance of SAT solvers on formulas expressed as the conjunction of both CNF constraints and variable-width XOR constraints (known as CNF-XOR formulas). In this paper, we present the first study of the runtime behavior of SAT solvers equipped with XOR-reasoning techniques on random CNF-XOR formulas. We empirically demonstrate that a state-of-the-art SAT solver scales exponentially on random CNF-XOR formulas across a wide range of XOR-clause densities, peaking around the empirical phase-transition location. On the theoretical front, we prove that the solution space of a random CNF-XOR formula 'shatters' at all nonzero XOR-clause densities into well-separated components, similar to the behavior seen in random CNF formulas known to be difficult for many SAT algorithms.

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