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.

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 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.

New CNF Features and Formula Classification

10.29007/b8t1 ◽  
2018 ◽  
Author(s):  
Enrique Alfonso ◽  
Norbert Manthey
Keyword(s):  
Machine Learning ◽  
Structural Information ◽  
Computation Time ◽  
The Other ◽  
Learning Approach ◽  
Sat Solvers ◽  
Random Decision Forests ◽  
Machine Learning Approach ◽  
Sat Solver ◽  
Cnf Formulas

In this paper we first present three new features for classifying CNF formulas. These features are based on the structural information of the formula and consider AND-gates as well as exactly-one constraints. Next, we use these features to construct a machine learning approach to select a SAT solver configuration for CNF formulas with random decision forests. Based on this classification task we can show that our new features are useful compared to existing features. Since the computation time for these features is small, the constructed classifier improves the performance of the SAT solvers on application and hand crafted benchmarks. On the other hand, the comparison shows that the set of new features also results in a better classification.

scholarly journals BIRD: Engineering an Efficient CNF-XOR SAT Solver and Its Applications to Approximate Model Counting

2019 ◽  
Vol 33 ◽  
pp. 1592-1599 ◽  
Author(s):  
Mate Soos ◽  
Kuldeep S. Meel
Keyword(s):  
Probabilistic Reasoning ◽  
State Of The Art ◽  
Fundamental Problem ◽  
Approximate Model ◽  
Affirmative Answer ◽  
The State ◽  
Boolean Formula ◽  
Wide Range ◽  
Model Counting ◽  
Sat Solver

Given a Boolean formula φ, the problem of model counting, also referred to as #SAT is to compute the number of solutions of φ. Model counting is a fundamental problem in artificial intelligence with a wide range of applications including probabilistic reasoning, decision making under uncertainty, quantified information flow, and the like. Motivated by the success of SAT solvers, there has been surge of interest in the design of hashing-based techniques for approximate model counting for the past decade. We profiled the state of the art approximate model counter ApproxMC2 and observed that over 99.99% of time is consumed by the underlying SAT solver, CryptoMiniSat. This observation motivated us to ask: Can we design an efficient underlying CNF-XOR SAT solver that can take advantage of the structure of hashing-based algorithms and would this lead to an efficient approximate model counter? The primary contribution of this paper is an affirmative answer to the above question. We present a novel architecture, called BIRD, to handle CNF-XOR formulas arising from hashingbased techniques. The resulting hashing-based approximate model counter, called ApproxMC3, employs the BIRD framework in its underlying SAT solver, CryptoMiniSat. To the best of our knowledge, we conducted the most comprehensive study of evaluation performance of counting algorithms involving 1896 benchmarks with computational effort totaling 86400 computational hours. Our experimental evaluation demonstrates significant runtime performance improvement for ApproxMC3 over ApproxMC2. In particular, we solve 648 benchmarks more than ApproxMC2, the state of the art approximate model counter and for all the formulas where both ApproxMC2 and ApproxMC3 did not timeout and took more than 1 seconds, the mean speedup is 284.40 – more than two orders of magnitude.

scholarly journals Unsatisfiability Proofs for Parallel SAT Solver Portfolios with Clause Sharing and Inprocessing

10.29007/68qz ◽  
2018 ◽  
Author(s):  
Tobias Philipp
Keyword(s):  
State Of The Art ◽  
Transition System ◽  
Systematic Search ◽  
Sat Solvers ◽  
Award Winning ◽  
Sat Solver ◽  
Simplification Techniques

State-of-the-art SAT solvers are highly tuned systematic-search procedures augmented with formula simplification techniques. They emit unsatisfiability proofs in the DRAT format to guarantee correctness of their answers. However, the DRAT format is inadequate to model some parallel SAT solvers such as the award-winning system \plingeling. In \plingeling, each solver in the portfolio applies clause addition and elimination techniques. Clause sharing is restricted to clauses that do not contain melted literals. In this paper, we develop a transition system that models the computation of such parallel portfolio solvers. The transition system allows us to formally reason about portfolio solvers, and we show that the formalism is sound and complete. Based on the formalism, we derive a new proof format, called parallel DRAT, which can be used to certify UNSAT answers.

scholarly journals Two SAT solvers for solving quantified Boolean formulas with an arbitrary number of quantifier alternations

2021 ◽  
Author(s):  
Roderick Bloem ◽  
Nicolas Braud-Santoni ◽  
Vedad Hadzic ◽  
Uwe Egly ◽  
Florian Lonsing ◽  
...  
Keyword(s):  
Arbitrary Number ◽  
State Of The Art ◽  
Simple Approach ◽  
Theory And Practice ◽  
Sat Solvers ◽  
Quantified Boolean Formulas ◽  
Boolean Formulas ◽  
Sat Solver ◽  
The Given ◽  
Novel Algorithm

AbstractIn recent years, expansion-based techniques have been shown to be very powerful in theory and practice for solving quantified Boolean formulas (QBF), the extension of propositional formulas with existential and universal quantifiers over Boolean variables. Such approaches partially expand one type of variable (either existential or universal) for obtaining a propositional abstraction of the QBF. If this formula is false, the truth value of the QBF is decided, otherwise further refinement steps are necessary. Classically, expansion-based solvers process the given formula quantifier-block wise and use one SAT solver per quantifier block. In this paper, we present a novel algorithm for expansion-based QBF solving that deals with the whole quantifier prefix at once. Hence recursive applications of the expansion principle are avoided and only two incremental SAT solvers are required. While our algorithm is naturally based on the $$\forall $$ ∀ Exp+Res calculus that is the formal foundation of expansion-based solving, it is conceptually simpler than present recursive approaches. Experiments indicate that the performance of our simple approach is comparable with the state of the art of QBF solving, especially in combination with other solving techniques.

CLINICAL AND FORENSIC ASPECTS OF PHARMACOBEZOARS

2020 ◽  
Vol 12 ◽  
Author(s):  
Francisco Basílio ◽  
Ricardo Jorge Dinis-Oliveira
Keyword(s):  
State Of The Art ◽  
Signs And Symptoms ◽  
Immediate Release ◽  
Diagnosis And Treatment ◽  
Blood Concentrations ◽  
Forensic Practice ◽  
Wide Range ◽  
Therapeutic Doses ◽  
Complete History ◽  
Lethal Blood

Background: Pharmacobezoars are specific types of bezoars formed when medicines, such as tablets, suspensions, and/or drug delivery systems, aggregate and may cause death by occluding airways with tenacious material or by eluting drugs resulting in toxic or lethal blood concentrations. Objective: This work aims to fully review the state-of-the-art regarding pathophysiology, diagnosis, treatment and other relevant clinical and forensic features of pharmacobezoars. Results: patients of a wide range of ages and in both sexes present with signs and symptoms of intoxications or more commonly gastrointestinal obstructions. The exact mechanisms of pharmacobezoar formation are unknown but is likely multifactorial. The diagnosis and treatment depend on the gastrointestinal segment affected and should be personalized to the medication and the underlying factor. A good and complete history, physical examination, image tests, upper endoscopy and surgery through laparotomy of the lower tract are useful for diagnosis and treatment. Conclusion: Pharmacobezoars are rarely seen in clinical and forensic practice. They are related to controlled or immediate-release formulations, liquid or non-digestible substances, in normal or altered digestive motility/anatomy tract, and in overdoses or therapeutic doses, and should be suspected in the presence of risk factors or patients taking drugs which may form pharmacobezoars.

Computers in Geology - 25 Years of Progress

1994 ◽  
Keyword(s):  
Computer Modeling ◽  
Quantitative Methods ◽  
State Of The Art ◽  
International Association ◽  
Mathematical Geology ◽  
25Th Anniversary ◽  
The Earth ◽  
Wide Range ◽  
History Of ◽  
Mapping Techniques

This volume vividly demonstrates the importance and increasing breadth of quantitative methods in the earth sciences. With contributions from an international cast of leading practitioners, chapters cover a wide range of state-of-the-art methods and applications, including computer modeling and mapping techniques. Many chapters also contain reviews and extensive bibliographies which serve to make this an invaluable introduction to the entire field. In addition to its detailed presentations, the book includes chapters on the history of geomathematics and on R.G.V. Eigen, the "father" of mathematical geology. Written to commemorate the 25th anniversary of the International Association for Mathematical Geology, the book will be sought after by both practitioners and researchers in all branches of geology.

scholarly journals Syllabification of the Divine Comedy

2021 ◽  
Vol 14 (3) ◽  
pp. 1-26
Author(s):  
Andrea Asperti ◽  
Stefano Dal Bianco
Keyword(s):  
Text Processing ◽  
Solution Space ◽  
Generative Models ◽  
Divine Comedy ◽  
Point Of View ◽  
Computer Assisted ◽  
Wide Range ◽  
The Divine Comedy ◽  
Left And Right ◽  
Assisted Analysis

We provide a syllabification algorithm for the Divine Comedy using techniques from probabilistic and constraint programming. We particularly focus on the synalephe , addressed in terms of the "propensity" of a word to take part in a synalephe with adjacent words. We jointly provide an online vocabulary containing, for each word, information about its syllabification, the location of the tonic accent, and the aforementioned synalephe propensity, on the left and right sides. The algorithm is intrinsically nondeterministic, producing different possible syllabifications for each verse, with different likelihoods; metric constraints relative to accents on the 10th, 4th, and 6th syllables are used to further reduce the solution space. The most likely syllabification is hence returned as output. We believe that this work could be a major milestone for a lot of different investigations. From the point of view of digital humanities it opens new perspectives on computer-assisted analysis of digital sources, comprising automated detection of anomalous and problematic cases, metric clustering of verses and their categorization, or more foundational investigations addressing, e.g., the phonetic roles of consonants and vowels. From the point of view of text processing and deep learning, information about syllabification and the location of accents opens a wide range of exciting perspectives, from the possibility of automatic learning syllabification of words and verses to the improvement of generative models, aware of metric issues, and more respectful of the expected musicality.

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