Marc Mézard, Andrea Montanari · 2009
Abstract Because of Cook's theorem, satisfiability lies at the heart of computational complexity theory. This chapter presents some selected research directions, focusing on ensembles of random satisfiability instances. When the density of constraints is increased, a phase transition between a SAT and an UNSAT phase take place. Properly tuned ensembles with a density close to the transition point provide a generator of particularly hard instances. The nature of this transition is discussed, and bounds on the critical density are obtained. On the algorithmic side, the discussion focuses on exhaustive search algorithms based on tree-search, and on random walk procedures.
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C.A.R. Hoare · Oxford University Research Archive (ORA) (University of Oxford) · 2015
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Alexander Koller, Kurt Mehlhorn, Joachmin Niehren et al. · 2009
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Uriel Feige, Elchanan Mossel, Dan Vilenchik · 2006
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J. N. Crossley, Anil Nerode · 1974
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Michael Genesereth, Eric Kao · Synthesis lectures on computer science · 2012
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William M. Spears · 1992
this paper is organized as follows. First, we describe the Davis Putnam algorithm. Second, we describe the NN algorithm. The essentials of Bayesian analysis are summarized in the fourth section. Section 5 explains the particular class of problems investigated, outlines the experiments performed, and describes the results. These results will enable us to make probabilistic claims concerning the satisfiability (or unsatisfiability) of problems from the problem class investigated, using the Bayesian analysis. We present an example of this analysis. Finally, we conclude with a summary and some remarks. 2 The Davis Putnam Algorithm
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Geng, Yu · Figshare · 2020
The Boolean Satisfiability Problem is also the first problem proven to be NP-complete. A problem is NP-complete if it belongs to the set (or "class" if you prefer) of the hardest problems in NP-hardest in the sense that every problem ever exists in NP can be reduced to them. (Thus being able to solve a NP-complete problem is equivalent to being able to solve every problem in NP).
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Xiaojuan Liao, Miyuki Koshimura · 2024
Apply satisfiability to a range of difficult problems The Boolean Satisfiability Problem (SAT) is one of the most famous and widely-studied problems in Boolean logic. Optimization versions of this problem include the Maximum Satisfiability Problem (MaxSAT) and its extensions, such as partial MaxSAT and weighted MaxSAT, which assess whether, and to what extent, a solution satisfies a given set of problems. Numerous applications of SAT and MaxSAT have emerged in fields related to logic and computing technology. Applied Satisfiability: Cryptography, Scheduling, and Coalitional Games outlines some of these applications in three specific fields. It offers a huge range of SAT applications and their possible impacts, allowing readers to tackle previously challenging optimization problems with a new selection of tools. Professionals and researchers in this field will find the scope of their computational solutions to otherwise intractable problems vastly increased. Applied Satisfiability readers will also find: Coding and problem-solving skills applicable to a variety of fieldsSpecific experiments and case studies that demonstrate the effectiveness of satisfiability-aided methodsChapters covering topics including cryptographic key recovery, various forms of scheduling, coalition structure generation, and many more Applied Satisfiability is ideal for researchers, graduate students, and practitioners in these fields looking to bring a new skillset to bear in their studies and careers.
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Richard Zippel · 2007
Among the NP-hard problems is 3SAT [2, 4], which asks if there exists a satisfying assignment for the Boolean variables in a conjunctive normal form formula. This paper gives a mapping of 3SAT problems into multi-dimensional definite integrals. These integrals take on values greater than 1 - # if the Boolean formula is satisfiable and less than 1/2 when it is not. They thus serve as e#ective indicators of the satisfiability of Boolean formulas. The number of dimensions of the integral is the same as the number of variables in the Boolean formula, so deterministic methods are unlikely to be successful. However, Monte Carlo techniques look promising. Regardless, the transformation of the purely combinatorial problem of satisfiability to the evaluation of a definite integral (of simple, continuous arguments), allows us to apply the vast arsenal of modern analysis to a problem that hitherto seemed an unlikely target. Given a Boolean formula, the problem of determining the existence of a...
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Hantao Zhang, Jian Zhang · Logic in Computer Science · 2025
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Ming‐Yang Kao · Encyclopedia of Algorithms · 2008
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Fontaine, Pascal, Mizuhito Ogawa, Sturm, Thomas et al. · Zenodo (CERN European Organization for Nuclear Research) · 2017
This upload consists of the source code of STROPSAT, a library for SubTROPical SATisfiability, and the experimental data of STROPSAT and Z3 on inequality constraints of SMT-LIB. The paper of STROPSAT was accepted at FroCos 2017 and the paper is publicly accessible at https://arxiv.org/abs/1706.09236.
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Michaël Guedj · WORLD SCIENTIFIC eBooks · 2019
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Pascal Fontaine, Mizuhito Ogawa, Thomas Sturm et al. · Lecture notes in computer science · 2017
Quantifier-free nonlinear arithmetic (QF_NRA) appears in many applications of satisfiability modulo theories solving (SMT). Accordingly, efficient reasoning for corresponding constraints in SMT theory solvers is highly relevant. We propose a new incomplete but efficient and terminating method to identify satisfiable instances. The method is derived from the subtropical method recently introduced in the context of symbolic computation for computing real zeros of single very large multivariate polynomials. Our method takes as input conjunctions of strict polynomial inequalities, which represent more than 40% of the QF_NRA section of the SMT-LIB library of benchmarks. The method takes an abstraction of polynomials as exponent vectors over the natural numbers tagged with the signs of the corresponding coefficients. It then uses, in turn, SMT to solve linear problems over the reals to heuristically find suitable points that translate back to satisfying points for the original problem. Systematic experiments on the SMT-LIB demonstrate that our method is not a sufficiently strong decision procedure by itself but a valuable heuristic to use within a portfolio of techniques.
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Juan Pablo Franco (19727544), Peter Bossaerts (230034), Carsten Murawski (174349) · Figshare · 2024
<p>Significant cluster-wise FWE-corrected (<i>p</i> < 0.05) clusters (using an uncorrected threshold of <i>p</i> < 0.001) from the <i>Unsatisfiable-Satisfiable</i> contrast. Coordinates are in MNI space.</p>
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Han-lim Choi, Chun-sang Teo · 2005
One of the key traits that distinguish intelligent beings is their ability to reason about the world based on acquired knowledge. In our quest for autonomy, where artificial agents have to operate in complex environments and make decisions without external intervention, such reasoning abilities are sometimes necessary. An agent that can acquire knowledge and reason based on such
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Emo Welzl · 2008
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Witold Pedrycz Giancarlo Succi · 2008
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Yacine Boufkhad, Thomas Hugel · Discrete Applied Mathematics · 2011
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