Ketema, Nahome · Zenodo (CERN European Organization for Nuclear Research) · 2025
This research presents the Y Tree, a structured logical model designed to evaluate Boolean SAT (Satisfiability) problems efficiently. By utilizing a hierarchical combination of AND, OR, and NOT gates, the Y Tree ensures a systematic approach to SAT solving while maintaining scalability. This paper outlines the theoretical foundation, algorithmic representation, experimental analysis, and complexity considerations of the method. The study also explores the implications of Y Tree in the context of P vs NP, discussing its potential for solving SAT in polynomial time. The work is protected under copyright, and unauthorized use is prohibited.
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Ketema, Nahom · Zenodo (CERN European Organization for Nuclear Research) · 2025
In next vertion we will explore about Y-tree method to solve SAT hti vetstion have error and is ristricted to use
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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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Budinich, Marco · arXiv (Cornell University) · 2017
We present a formulation of the Boolean Satisfiability Problem in spinor language that allows to give a necessary and sufficient condition for unsatisfiability. With this result we outline an algorithm to test for unsatisfiability with possibly interesting theoretical properties.
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Stepan G. Margaryan · arXiv (Cornell University) · 2023
This is the latest in a series of articles aimed at exploring the relationship between the complexity classes of P and NP. In the previous papers, we have proved that the sat CNF problem is polynomially reduced to the problem of finding a special covering for a set under the special decomposition of this set and vice versa. That is, these problems are polinomially equivalent. This means that the problem of finding a special covering for a set under a special decomposition of this set, is an NP-complete problem. We also described algorithmic procedures that determine whether there is a special covering for a set under a special decomposition of this set. In this article we prove that all these algorithmic procedures have polynomial time complexity with respect to the length of input data. In addition, we will describe an algorithm that, given any Boolean function in conjunctive normal form (CNF), determines in polynomial time whether this function is satisfiable. We will prove that the time complexity of this algorithm is bounded by the cube of the length of the input data. Also, if the function is not satisfiable, the algorithm deduces this result noting the reason for this result. We have implemented an algorithm in Python, and successfully tested it on Boolean functions represented in CNF with tens of thousands of variables and tens of thousands of clauses.
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Andrea Roli, Michela Milano · arXiv (Cornell University) · 2011
In this paper we present a new approach to solve the satisfiability problem (SAT), based on boolean networks (BN). We define a mapping between a SAT instance and a BN, and we solve SAT problem by simulating the BN dynamics. We prove that BN fixed points correspond to the SAT solutions. The mapping presented allows to develop a new class of algorithms to solve SAT. Moreover, this new approach suggests new ways to combine symbolic and connectionist computation and provides a general framework for local search algorithms.
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Algirdas Maknickas · Lecture notes in electrical engineering · 2013
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Stephen Hartley Math, Stephen J. Hartley · 2007
The Steiner system problem and the boolean satisfiability problem (SAT) are defined. Then it is shown how to convert a Steiner system problem into an instance of SAT. Solving the resulting SAT using genetic algorithms has not been very fruitful. Several reasons are suggested. This poor performance may tarnish the reputation of genetic algorithms as an effective and efficient method for solving combinatorial optimization problems such as SAT. To increase their exposure in the research community, Steiner system-derived SATs should be added to a genetic algorithm "test suite" or, alternatively, to the DIMACS Challenge set of SAT benchmark problems. INTRODUCTION Steiner systems are one of the many combinatorial block design problems [1]. We can state the existence condition for a Steiner system design as a boolean expression and use a genetic algorithm to search for an assignment to the variables of the expression that make it true. This particular design problem is a difficult one for gen...
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Marko Budinich · Theoretical Computer Science · 2019
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Nelson, Max (Max M.) · DSpace@MIT (Massachusetts Institute of Technology) · 2013
Thesis: M. Eng., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2013.
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tm2wrk · Bulletin of Miscellaneous Information (Royal Gardens Kew) · 2022
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Moustapha Diaby · arXiv (Cornell University) · 2008
In this paper, we present a new, graph-based modeling approach and a polynomial-sized linear programming (LP) formulation of the Boolean satisfiability problem (SAT). The approach is illustrated with a numerical example.
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Manuel Mejía-Lavalle, Adrià Ruiz, O. Joaquín Pérez et al. · 2015
A modified Hopfield Artificial Neural Network is proposed to solve effectively and efficiently Boolean Satisfiability (SAT) NP-hard problems. The proposed Neural Network is compared against other traditional methods employed in this field, such as Greedy SAT and Genetic Algorithms for SAT. The results show that the proposed network represents a good alternative given their output quality and response time speed.
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Pedrycz W, Succi G, Shai O · Archivio istituzionale della ricerca (Alma Mater Studiorum Università di Bologna) · 2002
This study is concerned with the Boolean satisfiability ISAT) problem and its solution in setting a hybrid computational intelligence environment of genetic and fuzzy computing. In this framework, FUZZY sets realize an embedding principle meaning that original two-valued (Boolean) functions under investigation are extended to their continuous countelparts resulting in the form of fuzzy (multivalued) functions. In the sequel, the SAT problem is refonnulated for the fuzzy functions and solved using a genetic algorithm (GA). It is shown that a GA, especially its recursive version, is an efficient tool for handling multivariable SAT problems. Thorough experiments revealed that the recursive version of the GA can solve SAT problems with more than 1000 variables.
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Vladimir V. Rybakov · Journal of Siberian Federal University Mathematics & Physics · 2021
We find a polynomial algorithm to solve SAT problem in Boolean Logic
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Benoît Hoessen · 2014
Cette these presente differentes techniques permettant de resoudre le probleme de satisfaction de formule booleenes utilisant le parallelisme et du calcul distribue. Dans le but de fournir une explication la plus complete possible, une presentation detaillee de l'algorithme CDCL est effectuee, suivi d'un etat de l'art. De ce point de depart, deux pistes sont explorees. La premiere est une amelioration d'un algorithme de type portfolio, permettant d'echanger plus d'informations sans perte d'efficacite. La seconde est une bibliotheque de fonctions avec son interface de programmation permettant de creer facilement des solveurs SAT distribues.
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Wenxuan Guo, Hui‐Ling Zhen, Xijun Li et al. · Machine Intelligence Research · 2023
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Alexander Rybalov · PRIKLADNAYa DISKRETNAYa MATEMATIKA · 2017
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Fadi Aloul, Karem A. Sakallah · Deep Blue (University of Michigan) · 2003
The last few years have seen an increasing interest in Boolean Satisfiability (SAT), spurred in part by the recent availability of powerful SAT solvers that are sufficiently efficient and robust to deal with large-scale SAT problem instances. This has led to the successful deployment of SAT technology into diverse electronic design automation applications. Nevertheless, a number of practical SAT instances remain difficult to solve and continue to defy even the best available SAT solvers. While the general SAT problem is intractable, our premise in this thesis is that SAT instances arising from real-world applications possess an innate structure that, once uncovered, can drastically simplify the instance. Motivated by this observation, we develop robust methods for detecting various structural properties of hard SAT instances and show how to utilize these properties to produce SAT algorithms that can scale with the increasing complexity of today's SAT instances. First, we show how to identify and break syntactic symmetries in SAT instances expressed in conjunctive normal form (CNF). The symmetries are broken by adding symmetry-breaking predicates to the SAT instance that significantly prune the search space. Second, we expose sparsity in SAT instances and show how to utilize that knowledge to efficiently identify orderings of variables that intelligently guide the decision engines in SAT solvers. Third, we observe that CNF constraints in a SAT instance exhibit self-similarity. In general, such constraints are explicitly represented which may exhaust available computer memory resulting in aborted runs. We address this problem by developing a backtrack search algorithm that implicitly represents the constraints using zero-suppressed binary decision diagrams. This allows the processing of sets of, rather than single, constraints. Finally, we observe that real-world SAT instances typically consist of specific structured CNF constraints, such as counting constraints, that can be efficiently encoded using pseudo-Boolean (PB) constraints. The use of PB constraints extends the application of SAT solvers to handle Boolean decision and optimization problems. We develop effective techniques for handling PB constraints. We have validated these claims and showed that utilizing structure can substantially speed up the search process and reduce the memory requirements for many SAT instances.
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Marko Budinich · arXiv (Cornell University) · 2019
We explore the relations between the Boolean Satisfiability Problem with $n$ Boolean variables and the orthogonal group $\mbox{O}(n)$. We show that all $2^n$ possible solutions induce involutions of $\mathbb{R}^n$ that lie in the compact, disconnected real manifold of dimension $n (n-1)/2$ of $\mbox{O}(n)$. This result in turn gives a new unsatisfiability test within group $\mbox{O}(n)$.
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