scholarly journals Seeking Practical CDCL Insights from Theoretical SAT Benchmarks

2018 ◽  
Author(s):  
Jan Elffers ◽  
Jesús Giráldez-Cru ◽  
Stephan Gocht ◽  
Jakob Nordström ◽  
Laurent Simon
Keyword(s):  
Systematic Study ◽  
Boolean Satisfiability ◽  
Proof System ◽  
Sat Solvers ◽  
Proof Search ◽  
Wide Range ◽  
Clause Learning ◽  
Resolution Proof ◽  
Shed Light

Over the last decades Boolean satisfiability (SAT) solvers based on conflict-driven clause learning (CDCL) have developed to the point where they can handle formulas with millions of variables. Yet a deeper understanding of how these solvers can be so successful has remained elusive. In this work we shed light on CDCL performance by using theoretical benchmarks, which have the attractive features of being a) scalable, b) extremal with respect to different proof search parameters, and c) theoretically easy in the sense of having short proofs in the resolution proof system underlying CDCL. This allows for a systematic study of solver heuristics and how efficiently they search for proofs. We report results from extensive experiments on a wide range of benchmarks. Our findings include several examples where theory predicts and explains CDCL behaviour, but also raise a number of intriguing questions for further study.

scholarly journals Divide and Conquer: Towards Faster Pseudo-Boolean Solving

2018 ◽  
Author(s):  
Jan Elffers ◽  
Jakob Nordström
Keyword(s):  
Boolean Satisfiability ◽  
Conflict Analysis ◽  
Divide And Conquer ◽  
Theoretical Strength ◽  
Integer Coefficient ◽  
Sat Solvers ◽  
Wide Range ◽  
Clause Learning

The last 20 years have seen dramatic improvements in the performance of algorithms for Boolean satisfiability---so-called SAT solvers---and today conflict-driven clause learning (CDCL) solvers are routinely used in a wide range of application areas. One serious short-coming of CDCL, however, is that the underlying method of reasoning is quite weak. A tantalizing solution is to instead use stronger pseudo-Boolean (PB) reasoning, but so far the promise of exponential gains in performance has failed to materialize---the increased theoretical strength seems hard to harness algorithmically, and in many applications CDCL-based methods are still superior. We propose a modified approach to pseudo-Boolean solving based on division instead of the saturation rule used in [Chai and Kuehlmann '05] and other PB solvers. In addition to resulting in a stronger conflict analysis, this also improves performance by keeping integer coefficient sizes down, and yields a very competitive solver as shown by the results in the Pseudo-Boolean Competitions 2015 and 2016.

HYBRID INCREMENTAL ALGORITHMS FOR BOOLEAN SATISFIABILITY

2012 ◽  
Vol 21 (06) ◽  
pp. 1250025 ◽  
Author(s):  
FLORIAN LETOMBE ◽  
JOAO MARQUES-SILVA
Keyword(s):  
Boolean Satisfiability ◽  
Equivalence Checking ◽  
Satisfiability Modulo Theory ◽  
Practical Applications ◽  
Sat Solvers ◽  
Hybrid Approaches ◽  
Software Model ◽  
Wide Range ◽  
Model Finding ◽  
Problem Instances

Boolean Satisfiability (SAT) solvers have been successfully applied to a wide range of practical applications, including hardware model checking, software model finding, equivalence checking, and planning, among many others. SAT solvers are also the building block of more sophisticated decision procedures, including Satisfiability Modulo Theory (SMT) solvers. The large number of applications of SAT yields ever more challenging problem instances, and motivate the development of more efficient algorithms. Recent work studied hybrid approaches for SAT, which involves integrating incomplete and complete SAT solvers. This paper proposes a number of improvements to hybrid SAT solvers. Experimental results demonstrate that the proposed optimizations are effective. The resulting algorithms in general perform better and, more importantly, are significantly more robust.

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 Towards Understanding and Harnessing the Potential of Clause Learning

2004 ◽  
Vol 22 ◽  
pp. 319-351 ◽  
Author(s):  
P. Beame ◽  
H. Kautz ◽  
A. Sabharwal
Keyword(s):  
Learning Algorithms ◽  
Proof System ◽  
Satisfiability Solvers ◽  
Planning And Design ◽  
Problem Description ◽  
Clause Learning ◽  
Level Problem ◽  
High Level ◽  
Resolution Proof

Efficient implementations of DPLL with the addition of clause learning are the fastest complete Boolean satisfiability solvers and can handle many significant real-world problems, such as verification, planning and design. Despite its importance, little is known of the ultimate strengths and limitations of the technique. This paper presents the first precise characterization of clause learning as a proof system (CL), and begins the task of understanding its power by relating it to the well-studied resolution proof system. In particular, we show that with a new learning scheme, CL can provide exponentially shorter proofs than many proper refinements of general resolution (RES) satisfying a natural property. These include regular and Davis-Putnam resolution, which are already known to be much stronger than ordinary DPLL. We also show that a slight variant of CL with unlimited restarts is as powerful as RES itself. Translating these analytical results to practice, however, presents a challenge because of the nondeterministic nature of clause learning algorithms. We propose a novel way of exploiting the underlying problem structure, in the form of a high level problem description such as a graph or PDDL specification, to guide clause learning algorithms toward faster solutions. We show that this leads to exponential speed-ups on grid and randomized pebbling problems, as well as substantial improvements on certain ordering formulas.

scholarly journals Analysis of comparative effectiveness of state-of-the-art heuristics for CDCL SAT solvers

2021 ◽  
Author(s):  
S. Kochemazov
Keyword(s):  
Comparative Effectiveness ◽  
Major Part ◽  
State Of The Art ◽  
Learning Algorithms ◽  
Boolean Satisfiability ◽  
Satisfiability Problem ◽  
Sat Solvers ◽  
Boolean Satisfiability Problem ◽  
Clause Learning ◽  
Good For

The Conflict-Driven Clause Learning algorithms for solving the Boolean satisfiability problem comprise the major part of the methods used to solve various instances of the problems that arise in industry and science. In recent years there have been proposed several major heuristics for these algorithms which are assumed to be de facto good for the solvers’ performance over diverse sets of benchmarks. The goal of this paper is to evaluate the contribution of each separate heuristic to the performance of a state-of-the-art solver, see the extent to which they are beneficial, and figure out if the heuristics have any particular features that need to be taken into account.

COMPLETE SAT-BASED MODEL CHECKING FOR CONTEXT-FREE PROCESSES

2010 ◽  
Vol 21 (02) ◽  
pp. 115-134
Author(s):  
GENG-DIAN HUANG ◽  
BOW-YAW WANG
Keyword(s):  
Model Checking ◽  
Software Verification ◽  
Boolean Satisfiability ◽  
Local Model ◽  
Sat Solvers ◽  
Proof Search ◽  
Software Programs ◽  
Context Free ◽  
Local Model Checking

A complete SAT-based model checking algorithm for context-free processes is presented. We reduce proof search in local model checking to Boolean satisfiability. Bounded proof search can therefore be performed by SAT solvers. Moreover, the completeness of proof search is reduced to Boolean unsatisfiability and hence can be checked by SAT solvers. By encoding the local model checking algorithm in [13], SAT solvers are able to verify properties in the universal fragment of alternation-free µ-calculus formulae on context-free processes. Since software programs can be modeled by context-free processes, our result demonstrates that a purely SAT-based algorithm for software verification is indeed possible.

Sentence-Based Experience Logging in New Hearing Aid Users

2020 ◽  
Vol 29 (3S) ◽  
pp. 631-637
Author(s):  
Katja Lund ◽  
Rodrigo Ordoñez ◽  
Jens Bo Nielsen ◽  
Dorte Hammershøi
Keyword(s):  
Hearing Aid ◽  
Patient Experiences ◽  
Online Tool ◽  
Rehabilitation Process ◽  
Hearing Rehabilitation ◽  
Clinical Observations ◽  
Hearing Aid Use ◽  
Wide Range ◽  
Insight Into ◽  
Shed Light

Purpose The aim of this study was to develop a tool to gain insight into the daily experiences of new hearing aid users and to shed light on aspects of aided performance that may not be unveiled through standard questionnaires. Method The tool is developed based on clinical observations, patient experiences, expert involvement, and existing validated hearing rehabilitation questionnaires. Results An online tool for collecting data related to hearing aid use was developed. The tool is based on 453 prefabricated sentences representing experiences within 13 categories related to hearing aid use. Conclusions The tool has the potential to reflect a wide range of individual experiences with hearing aid use, including auditory and nonauditory aspects. These experiences may hold important knowledge for both the patient and the professional in the hearing rehabilitation process.

scholarly journals Beyond cultural and geographical proximity: delving into the factors that influence the dynamics of academic relationships between students in higher education

2021 ◽  
Author(s):  
José-Vicente Tomás-Miquel ◽  
Jordi Capó-Vicedo
Keyword(s):  
University Students ◽  
Academic Research ◽  
Past Research ◽  
Academic Networks ◽  
Level Data ◽  
Wide Range ◽  
Specific Stage ◽  
The University ◽  
Proximity Dimensions ◽  
Shed Light

AbstractScholars have widely recognised the importance of academic relationships between students at the university. While much of the past research has focused on studying their influence on different aspects such as the students’ academic performance or their emotional stability, less is known about their dynamics and the factors that influence the formation and dissolution of linkages between university students in academic networks. In this paper, we try to shed light on this issue by exploring through stochastic actor-oriented models and student-level data the influence that a set of proximity factors may have on formation of these relationships over the entire period in which students are enrolled at the university. Our findings confirm that the establishment of academic relationships is derived, in part, from a wide range of proximity dimensions of a social, personal, geographical, cultural and academic nature. Furthermore, and unlike previous studies, this research also empirically confirms that the specific stage in which the student is at the university determines the influence of these proximity factors on the dynamics of academic relationships. In this regard, beyond cultural and geographic proximities that only influence the first years at the university, students shape their relationships as they progress in their studies from similarities in more strategic aspects such as academic and personal closeness. These results may have significant implications for both academic research and university policies.

scholarly journals Messianism, rationalism and inter-Asian connections: The Majalis-i Jahangiri (1608–11) and the socio-intellectual history of the Mughal ‘ulama

2017 ◽  
Vol 54 (3) ◽  
pp. 317-338 ◽  
Author(s):  
Corinne Lefèvre
Keyword(s):  
Central Asia ◽  
Intellectual History ◽  
State Building ◽  
Specific Role ◽  
Wide Range ◽  
History Of ◽  
Muslim Intellectuals ◽  
Shed Light

Relying on the Majalis-i Jahangiri (1608–11) by ʿAbd al-Sattar b. Qasim Lahauri, this essay explores some of the discussions the Mughal Emperor Jahangir (r. 1605–27) conducted with a wide range of scholars, from Brahmans and ʿulama to Jesuit padres and Jewish savants. By far the most numerous, the debates bearing on Islam and involving Muslim intellectuals are especially significant on several accounts. First, because they illuminate how, following in the steps of his father Akbar (r. 1556–605), Jahangir was able to conciliate his messianic claims with a strong engagement with reason and to turn this combination into a formidable instrument for confession and state building. These conversations also provide promising avenues to think afresh the socio-intellectual history of the Mughal ʿulama inasmuch as they capture the challenges and adjustments attendant on imperial patronage, depict the jockeying for influence and positions among intellectuals (particularly between Indo-Muslim and Iranian lettrés), and shed light on relatively little known figures or on unexplored facets of more prominent individuals. In addition, the specific role played by scholars hailing from Iran—and, to a lesser extent, from Central Asia—in the juridical-religious disputes of the Indian court shows how crucial inter-Asian connections and networks were in the fashioning of Mughal ideology but also the ways in which the ongoing flow of émigré ʿulama was disciplined before being incorporated into the empire.

scholarly journals Book Review: Islam: A Worldwide Encyclopedia

2017 ◽  
Vol 57 (2) ◽  
pp. 151
Author(s):  
Paul Fehrmann
Keyword(s):  
International Law ◽  
Common Ground ◽  
Controversial Issues ◽  
Islamic Studies ◽  
Law And Politics ◽  
Wide Range ◽  
Senior Researcher ◽  
Shed Light ◽  
Academic Debate

It is clear that the world of Islam is profoundly important, and also that there are wide and conflicting views on Islam today. Similarly, it seems clear that we should pursue efforts to promote the understanding of Islam. In response, a goal of the four volume Islam: A Worldwide Encyclopedia (IAWE) is to give “basic information on Islam” and to “shed light” on “controversial issues” (xxvii). In his opening comments, the editor, a Professor of International Law and Politics at Eskişehir Osmangazi University and Senior Researcher at the Wise Men Center for Strategic Research in Turkey, notes that there have been “a wide range of different interpretations and variations of Islam throughout history” (xxvii). He suggests that Muslims need to revive the “strong tradition of academic debate” that was integral to Islamic studies “in early decades of Islam,” and affirms support for the “diverse and plural nature of contemporary Islamic scholarship” (xxviii). At the same time, he is concerned that “disputed issues” may lead to “biases and stereotypes in the minds of Western people,” and hopes that this new resource can both “contribute to the pursuit of a common ground” between those of different faiths, and help a Western audience become more familiar with what Islam has to offer (xxviii).

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