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Boolean satisfiability from theoretical hardness to practical success

Sharad Malik, Lintao Zhang
2009 Communications of the ACM  
Given its theoretical hardness, the practical success of SAT has come as a surprise to many in the computer science community.  ...  This leads us to a defi nition of the Boolean Satisfi ability problem (also referred to as Propositional Satisfi ability or just Satisfi ability, and abbreviated as SAT): Given a formula, fi nd a satisfying  ... 
doi:10.1145/1536616.1536637 fatcat:z3zi5mkjxrbwthbntlzwdayr6m

SAT and Interactions (Dagstuhl Seminar 16381)

Olaf Beyersdorff, Nadia Creignou, Uwe Egly, Heribert Vollmer, Marc Herbstritt
2017 Dagstuhl Reports  
The seminar brought together researchers from different areas from theoretical computer science involved with various aspects of satisfiability.  ...  A key objective of the seminar has been to initiate or consolidate discussions among the different groups for a fresh attack on one of the most important problems in theoretical computer science and mathematics  ...  Variable expansion relies on the successive elimination of variables from a QBF until the formula reduces to true or false.  ... 
doi:10.4230/dagrep.6.9.74 dblp:journals/dagstuhl-reports/BeyersdorffCEV16 fatcat:boyfegt3erba5j5hbdheironmu

What's hard about Boolean Functional Synthesis [article]

S. Akshay, Supratik Chakraborty, Shubham Goel, Sumith Kulal, and Shetal Shah
2018 arXiv   pre-print
Given this inherent hardness, what does one do to solve the problem?  ...  Given a relational specification between Boolean inputs and outputs, the goal of Boolean functional synthesis is to synthesize each output as a function of the inputs such that the specification is met  ...  In this paper, we re-examine the Boolean functional synthesis problem from both theoretical and practical perspectives.  ... 
arXiv:1804.05507v2 fatcat:fqne5bnv7jf3zn7aitenhb6n6y

FourierSAT: A Fourier Expansion-Based Algebraic Framework for Solving Hybrid Boolean Constraints

Anastasios Kyrillidis, Anshumali Shrivastava, Moshe Vardi, Zhiwei Zhang
2020 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
The Boolean SATisfiability problem (SAT) is of central importance in computer science.  ...  expectations of running time.To address the issues above, we design FourierSAT, an incomplete SAT solver based on Fourier analysis of Boolean functions, a technique to represent Boolean functions by multilinear  ...  Solving SAT efficiently is of utmost significance in computer science, both from a theoretical and a practical perspective.  ... 
doi:10.1609/aaai.v34i02.5515 fatcat:iqq6ys6i6zfv7jwwskqka23zve

Implementing Valiant's learnability theory using random sets

E. M. Oblow
1992 Machine Learning  
Some theoretical and empirical analyses are presented to demonstrate the convergent pac-learnability and sample complexity of this psi-algorithm.  ...  The random set version of this theory is used to develop an algorithm which is a particularly efficient search scheme.  ...  Acknowledgments The author wishes to thank Oscar Manley of the Department of Energy's Office of Basic Energy Sciences for his continuing financial support of random set research.  ... 
doi:10.1007/bf00994005 fatcat:mncbay6xovhhza53hg2hgm5cxy

The Boolean Satisfiability Problem [article]

Yu Geng
2020 Figshare  
The Boolean Satisfiability Problem is also the first problem proven to be NP-complete.  ...  (Thus being able to solve a NP-complete problem is equivalent to being able to solve every problem in NP).  ...  The Boolean Satisfiability Problem (SAT) • Given: A Boolean formula F(x 1 , x 2 , x 3 , …, x n ) • Can F evaluate to 1 (true)? -Is F satisfiable?  ... 
doi:10.6084/m9.figshare.12331172.v1 fatcat:ky6vwo7gm5h3vfovcrpoknfovm

Generalized Graph Colorability and Compressibility of Boolean Formulae [chapter]

Richard Nock, Pascal Jappy, Jean Sallantin
1998 Lecture Notes in Computer Science  
We prove that approximating the minimally consistent DNF formula, and a generalization of graph colorability, is very hard.  ...  Theoretically speaking, our result rules out the existence of efficient deterministic Occam's razor algorithms for DNF.  ...  It means that there exists a reduction from "SAT" to Opt(Independent set) such that -Any graph G obtained from a satisfiable instance of "SAT" satisfies α(G ) = g.  ... 
doi:10.1007/3-540-49381-6_26 fatcat:wt63bayrozakbljpf6yloto42y

Modal Nonmonotonic Logics Revisited: Efficient Encodings for the Basic Reasoning Tasks [chapter]

Thomas Eiter, Volker Klotz, Hans Tompits, Stefan Woltran
2002 Lecture Notes in Computer Science  
Although these formalisms are extensively studied from a theoretical point of view, most of these approaches lack generally available solvers thus far.  ...  Since there are now efficient QBF-solvers, this reduction technique yields a practicably relevant approach to build prototype reasoning systems for these formalisms.  ...  From a theoretical point of view, the feasibility of the current approach relies on the observation that the evaluation problem of quantified Boolean formulas, qsat, is PSPACE-complete, so any decision  ... 
doi:10.1007/3-540-45616-3_8 fatcat:5yzrmskpq5a45j7tzrch6qj6ja

Lazy Clause Generation: Combining the Power of SAT and CP (and MIP?) Solving [chapter]

Peter J. Stuckey
2010 Lecture Notes in Computer Science  
Boolean satisfiability (SAT) solving allows the construction of a graph of inferences made in order to determine and record effective nogoods which prevent the searching of similar parts of the problem  ...  , as well as the determination of those variables which form a tightly connected hard part of the problem, thus allowing highly effective automatic search strategies concentrating on these hard parts.  ...  The success of finite domain propagation in solving hard combinatorial problems arises from these good trade-offs, and programmable search, and has defined the success of constraint programming (CP).  ... 
doi:10.1007/978-3-642-13520-0_3 fatcat:bwlxjkj54vfwxhoqmtnd4i3hmy

What's Hard About Boolean Functional Synthesis? [chapter]

S. Akshay, Supratik Chakraborty, Shubham Goel, Sumith Kulal, Shetal Shah
2018 Lecture Notes in Computer Science  
Given this inherent hardness, what does one do to solve the problem?  ...  Given a relational specification between Boolean inputs and outputs, the goal of Boolean functional synthesis is to synthesize each output as a function of the inputs such that the specification is met  ...  Acknowledgements: We are thankful to Ajith John, Kuldeep Meel, Mate Soos, Ocan Sankur, Lucas Martinelli Tabajara and Markus Rabe for useful discussions and for providing us with various software tools  ... 
doi:10.1007/978-3-319-96145-3_14 fatcat:ws2spinhwbeljamzk5cjti634a

SAT-based Compressive Sensing [article]

Ramin Ayanzadeh, Milton Halem, Tim Finin
2019 arXiv   pre-print
The original problem of compressive sensing in sparse recovery is NP-hard; therefore, in addition to restrictions for the uniqueness of the sparse solution, the coding matrix has also to satisfy additional  ...  In practice, such constraints are not only intractable to be verified but also invalid in broad applications.  ...  We would like to thank the NSF fund-ed Center for Hybrid Multicore Productivity Research for access support to IBM Min-sky cluster.  ... 
arXiv:1903.03650v2 fatcat:46z7qte4qrfurkboolh4td3vqi

Analyses and Algorithms for Predecessor and Control Problems for Boolean Networks of Bounded Indegree

Tatsuya Akutsu, Morihiro Hayashida, Shu-Qin Zhang, Wai-Ki Ching, Michael K. Ng
2008 IPSJ Transactions on Bioinformatics  
We study the predecessor and control problems for Boolean networks (BNs).  ...  In this paper, we focus on BNs of bounded indegree and show some hardness results on the computational complexity of the predecessor and control problems.  ...  Acknowledgments TA was partially supported by a Grant-in-Aid "Systems Genomics" from MEXT and by the Cell Array Project from NEDO, Japan.  ... 
doi:10.2197/ipsjtbio.1.23 fatcat:ouyb7bzm6jawhihlbuexuif3aq

Understanding Boolean Function Learnability on Deep Neural Networks [article]

Anderson R. Tavares, Pedro Avelar, João M. Flach, Marcio Nicolau, Luis C. Lamb, Moshe Vardi
2021 arXiv   pre-print
learn, possibly due to the fewer positive (satisfying) examples available; and (iii) interestingly, underconstrained 3-CNF formulas are more challenging to learn than overconstrained ones.  ...  This paper addresses the understudied subject of how, in practice, such formulas can be learned by deep neural networks.  ...  Moshe Vardi is supported in part by NSF grants IIS-1527668, CCF-1704883, IIS-1830549, DoD MURI grant N00014-20-1-2787, and an award from the Maryland Procurement Office.  ... 
arXiv:2009.05908v2 fatcat:ry2evqrirnefzizzhppafjtx5m

On Variable Orderings in MCSAT for Non-linear Real Arithmetic : (extended abstract)

Jasper Nalbach, Gereon Lukas Kremer, Erika Ábrahám
2019 CEUR Workshop Proceedings  
The latter explanations are added to the original formula to exclude theory-inconsistent Boolean models from the further search.  ...  During this search, the SAT solver 1 passes theory constraints corresponding to the current (possibly partial) Boolean model to the theory solver.  ...  Dynamic variable orderings also give rise to theoretical questions about the completeness of MCSAT.  ... 
doi:10.18154/rwth-conv-240068 fatcat:245p44r2vngf7j2w5puijg3tda

Graph Neural Networks and Boolean Satisfiability [article]

Benedikt Bünz, Matthew Lamm
2017 arXiv   pre-print
In this paper we explore whether or not deep neural architectures can learn to classify Boolean satisfiability (SAT). We devote considerable time to discussing the theoretical properties of SAT.  ...  of satisfiability.  ...  In section 3 we discuss some theoretical properties of Boolean satisfiability, emphasizing implications for training learners on weakly-supervised graphs to discover properties of satisfiability.  ... 
arXiv:1702.03592v1 fatcat:gah2gjalzvb6bgz35qwp663u3i
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