scholarly journals Combining Conflict-Driven Clause Learning and Chronological Backtracking for Propositional Model Counting

10.29007/vgg4 ◽  
2019 ◽  
Author(s):  
Sibylle Möhle ◽  
Armin Biere
Keyword(s):  
State Of The Art ◽  
Search Space ◽  
Formal Proof ◽  
Propositional Formula ◽  
Sat Solvers ◽  
Model Counting ◽  
Clause Learning ◽  
Solver Performance

In propositional model counting, also named #SAT, the search space needs to be explored exhaustively, in contrast to SAT, where the task is to determine whether a propositional formula is satisfiable. While state-of-the-art SAT solvers are based on non- chronological backtracking, it has also been shown that backtracking chronologically does not significantly degrade solver performance. Hence investigating the combination of chronological backtracking with conflict-driven clause learning (CDCL) for #SAT seems evident. We present a calculus for #SAT combining chronological backtracking with CDCL and provide a formal proof of its correctness.

scholarly journals GANAK: A Scalable Probabilistic Exact Model Counter

2019 ◽  
Author(s):  
Shubham Sharma ◽  
Subhajit Roy ◽  
Mate Soos ◽  
Kuldeep S. Meel
Keyword(s):  
Probabilistic Reasoning ◽  
State Of The Art ◽  
Fundamental Problem ◽  
Approximate Model ◽  
Boolean Formula ◽  
Sat Solvers ◽  
Exact Model ◽  
Universal Hashing ◽  
Model Counting ◽  
Dynamic Decomposition

Given a Boolean formula F, the problem of model counting, also referred to as #SAT, seeks to compute the number of solutions of F. Model counting is a fundamental problem with a wide variety of applications ranging from planning, quantified information flow to probabilistic reasoning and the like. The modern #SAT solvers tend to be either based on static decomposition, dynamic decomposition, or a hybrid of the two. Despite dynamic decomposition based #SAT solvers sharing much of their architecture with SAT solvers, the core design and heuristics of dynamic decomposition-based #SAT solvers has remained constant for over a decade. In this paper, we revisit the architecture of the state-of-the-art dynamic decomposition-based #SAT tool, sharpSAT, and demonstrate that by introducing a new notion of probabilistic component caching and the usage of universal hashing for exact model counting along with the development of several new heuristics can lead to significant performance improvement over state-of-the-art model-counters. In particular, we develop GANAK, a new scalable probabilistic exact model counter that outperforms state-of-the-art exact and approximate model counters sharpSAT and ApproxMC3 respectively, both in terms of PAR-2 score and the number of instances solved. Furthermore, in our experiments, the model count returned by GANAK was equal to the exact model count for all the benchmarks. Finally, we observe that recently proposed preprocessing techniques for model counting benefit exact model counters while hurting the performance of approximate model counters.

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 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.

scholarly journals RECPARSER: A Recursive Semantic Parsing Framework for Text-to-SQL Task

2020 ◽  
Author(s):  
Yu Zeng ◽  
Yan Gao ◽  
Jiaqi Guo ◽  
Bei Chen ◽  
Qian Liu ◽  
...  
Keyword(s):  
State Of The Art ◽  
Search Space ◽  
Layer By Layer ◽  
Semantic Parsing ◽  
Query Generation ◽  
Sql Query ◽  
Generation Problem

Neural semantic parsers usually fail to parse long and complicated utterances into nested SQL queries, due to the large search space. In this paper, we propose a novel recursive semantic parsing framework called RECPARSER to generate the nested SQL query layer-by-layer. It decomposes the complicated nested SQL query generation problem into several progressive non-nested SQL query generation problems. Furthermore, we propose a novel Question Decomposer module to explicitly encourage RECPARSER to focus on different components of an utterance when predicting SQL queries of different layers. Experiments on the Spider dataset show that our approach is more effective compared to the previous works at predicting the nested SQL queries. In addition, we achieve an overall accuracy that is comparable with state-of-the-art approaches.

scholarly journals Scaling Up AND/OR Abstraction Sampling

2020 ◽  
Author(s):  
Kalev Kask ◽  
Bobak Pezeshki ◽  
Filjor Broka ◽  
Alexander Ihler ◽  
Rina Dechter
Keyword(s):  
Importance Sampling ◽  
State Of The Art ◽  
Empirical Evaluation ◽  
Search Space ◽  
Scaling Up ◽  
Sampling Scheme ◽  
Search Spaces

Abstraction Sampling (AS) is a recently introduced enhancement of Importance Sampling that exploits stratification by using a notion of abstractions: groupings of similar nodes into abstract states. It was previously shown that AS performs particularly well when sampling over an AND/OR search space; however, existing schemes were limited to ``proper'' abstractions in order to ensure unbiasedness, severely hindering scalability. In this paper, we introduce AOAS, a new Abstraction Sampling scheme on AND/OR search spaces that allow more flexible use of abstractions by circumventing the properness requirement. We analyze the properties of this new algorithm and, in an extensive empirical evaluation on five benchmarks, over 480 problems, and comparing against other state of the art algorithms, illustrate AOAS's properties and show that it provides a far more powerful and competitive Abstraction Sampling framework.

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 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.

Genetic Diversity as an Objective in Multi-Objective Evolutionary Algorithms

2003 ◽  
Vol 11 (2) ◽  
pp. 151-167 ◽  
Author(s):  
Andrea Toffolo ◽  
Ernesto Benini
Keyword(s):  
Genetic Diversity ◽  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Selection Pressure ◽  
Evaluation Method ◽  
State Of The Art ◽  
Search Space ◽  
Test Problems ◽  
Multi Objective ◽  
Diversity Evaluation

A key feature of an efficient and reliable multi-objective evolutionary algorithm is the ability to maintain genetic diversity within a population of solutions. In this paper, we present a new diversity-preserving mechanism, the Genetic Diversity Evaluation Method (GeDEM), which considers a distance-based measure of genetic diversity as a real objective in fitness assignment. This provides a dual selection pressure towards the exploitation of current non-dominated solutions and the exploration of the search space. We also introduce a new multi-objective evolutionary algorithm, the Genetic Diversity Evolutionary Algorithm (GDEA), strictly designed around GeDEM and then we compare it with other state-of-the-art algorithms on a well-established suite of test problems. Experimental results clearly indicate that the performance of GDEA is top-level.

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.

Chapter 13. Symmetry and Satisfiability

2021 ◽  
Author(s):  
Karem A. Sakallah
Keyword(s):  
Group Theory ◽  
Normal Form ◽  
Boolean Functions ◽  
Search Algorithm ◽  
Conjunctive Normal Form ◽  
Search Space ◽  
Decision Problems ◽  
Mathematical Language ◽  
Sat Solvers ◽  
Speed Up

Symmetry is at once a familiar concept (we recognize it when we see it!) and a profoundly deep mathematical subject. At its most basic, a symmetry is some transformation of an object that leaves the object (or some aspect of the object) unchanged. For example, a square can be transformed in eight different ways that leave it looking exactly the same: the identity “do-nothing” transformation, 3 rotations, and 4 mirror images (or reflections). In the context of decision problems, the presence of symmetries in a problem’s search space can frustrate the hunt for a solution by forcing a search algorithm to fruitlessly explore symmetric subspaces that do not contain solutions. Recognizing that such symmetries exist, we can direct a search algorithm to look for solutions only in non-symmetric parts of the search space. In many cases, this can lead to significant pruning of the search space and yield solutions to problems which are otherwise intractable. This chapter explores the symmetries of Boolean functions, particularly the symmetries of their conjunctive normal form (CNF) representations. Specifically, it examines what those symmetries are, how to model them using the mathematical language of group theory, how to derive them from a CNF formula, and how to utilize them to speed up CNF SAT solvers.

Sign in / Sign up

Export Citation Format

Share Document