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Satisfiability problem (SAT) is a cornerstone of computational complexity with broad industrial applications, and it remains challenging to optimize modern SAT solvers in real-world settings due to their intricate architectures. While…

Artificial Intelligence · Computer Science 2025-07-31 Yiwen Sun , Furong Ye , Zhihan Chen , Ke Wei , Shaowei Cai

We study the performance of stochastic local search algorithms for random instances of the $K$-satisfiability ($K$-SAT) problem. We introduce a new stochastic local search algorithm, ChainSAT, which moves in the energy landscape of a…

Data Structures and Algorithms · Computer Science 2009-11-13 Mikko Alava , John Ardelius , Erik Aurell , Petteri Kaski , Supriya Krishnamurthy , Pekka Orponen , Sakari Seitz

Upper bounds on the maximum number of codewords in a binary code of a given length and minimum Hamming distance are considered. New bounds are derived by a combination of linear programming and counting arguments. Some of these bounds…

Information Theory · Computer Science 2007-07-13 Beniamin Mounits , Tuvi Etzion , Simon Litsyn

I describe one quantum approach to solving 3-satisfiability (3-SAT), the well known problem in computer science. The approach is based on repeatedly measuring the truth value of the clauses forming the 3-SAT proposition using a…

Quantum Physics · Physics 2015-09-03 Simon Benjamin

Given $k$ collections of 2SAT clauses on the same set of variables $V$, can we find one assignment that satisfies a large fraction of clauses from each collection? We consider such simultaneous constraint satisfaction problems, and design…

Data Structures and Algorithms · Computer Science 2014-07-30 Amey Bhangale , Swastik Kopparty , Sushant Sachdeva

We consider the problem of solving floating-point constraints obtained from software verification. We present UppSAT --- a new implementation of a systematic approximation refinement framework [ZWR17] as an abstract SMT solver. Provided…

Logic in Computer Science · Computer Science 2017-12-12 Aleksandar Zeljic , Peter Backeman , Christoph M. Wintersteiger , Philipp Ruemmer

An O(n+m)-time algorithm is presented for counting the number of models of a two Conjunctive Normal Form Formula F that represents a Cactus graph, where n is the number of variables and m is the number of clauses of F. Although, it was…

Logic in Computer Science · Computer Science 2017-03-01 M. A. López , J. R. Marcial , G. De Ita , H. A. Montes-Venegas , R. Alejo

We consider semidefinite programming (SDP) approaches for solving the maximum satisfiability problem (MAX-SAT) and the weighted partial MAX-SAT. It is widely known that SDP is well-suited to approximate the (MAX-)2-SAT. Our work shows the…

Optimization and Control · Mathematics 2023-02-15 Lennart Sinjorgo , Renata Sotirov

Subset-Sum and k-SAT are two of the most extensively studied problems in computer science, and conjectures about their hardness are among the cornerstones of fine-grained complexity. One of the most intriguing open problems in this area is…

Data Structures and Algorithms · Computer Science 2021-02-22 Amir Abboud , Karl Bringmann , Danny Hermelin , Dvir Shabtay

The {\em maximum cardinality} and {\em maximum weight matching} problems can be solved in time $\tilde{O}(m\sqrt{n})$, a bound that has resisted improvement despite decades of research. (Here $m$ and $n$ are the number of edges and…

Data Structures and Algorithms · Computer Science 2011-12-06 Ran Duan , Seth Pettie , Hsin-Hao Su

It is crucial to generate crafted SAT formulas with predefined solutions for the testing and development of SAT solvers since many SAT formulas from real-world applications have solutions. Although some generating algorithms have been…

Artificial Intelligence · Computer Science 2019-02-27 Yamin Hu , Wenjian Luo , Junteng Wang

In this paper, we extend the Maximum Satisfiability (MaxSAT) problem to {\L}ukasiewicz logic. The MaxSAT problem for a set of formulae {\Phi} is the problem of finding an assignment to the variables in {\Phi} that satisfies the maximum…

Logic in Computer Science · Computer Science 2018-06-12 Mohamed El Halaby , Areeg Abdalla

In this paper, we introduce an exact algorithm with a time complexity of $O^*(1.325^m)$ for the {\sc weighted mutually exclusive maximum set cover} problem, where $m$ is the number of subsets in the problem. This is an NP-hard motivated and…

Data Structures and Algorithms · Computer Science 2014-01-27 Songjian Lu , Xinghua Lu

The CNF formula satisfiability problem (CNF-SAT) has been reduced to many fundamental problems in P to prove tight lower bounds under the Strong Exponential Time Hypothesis (SETH). Recently, the works of Abboud, Hansen, Vassilevska W. and…

Computational Complexity · Computer Science 2020-08-31 Daniel Gibney , Gary Hoppenworth , Sharma V. Thankachan

Various "hardness" measures have been studied for resolution, providing theoretical insight into the proof complexity of resolution and its fragments, as well as explanations for the hardness of instances in SAT solving. In this report we…

Computational Complexity · Computer Science 2014-02-18 Olaf Beyersdorff , Oliver Kullmann

The Boolean constraint satisfaction problem 3-SAT is arguably the canonical NP-complete problem. In contrast, 2-SAT can not only be decided in polynomial time, but in fact in deterministic linear time. In 2006, Bravyi proposed a physically…

Quantum Physics · Physics 2016-10-25 Niel de Beaudrap , Sevag Gharibian

We study the Boolean Satisfiability problem (SAT) in the framework of diversity, where one asks for multiple solutions that are mutually far apart (i.e., sufficiently dissimilar from each other) for a suitable notion of…

Data Structures and Algorithms · Computer Science 2024-12-16 Neeldhara Misra , Harshil Mittal , Ashutosh Rai

A pair of unit clauses is called conflicting if it is of the form $(x)$, $(\bar{x})$. A CNF formula is unit-conflict free (UCF) if it contains no pair of conflicting unit clauses. Lieberherr and Specker (J. ACM 28, 1981) showed that for…

Data Structures and Algorithms · Computer Science 2015-05-18 R. Crowston , G. Gutin , M. Jones , A. Yeo

The Boolean satisfiability problem (SAT) is of central importance in both theory and practice. Yet, most provable guarantees for quantum algorithms rely exclusively on Grover-type methods that cap the possible advantage at only quadratic…

Quantum Physics · Physics 2025-11-14 Franz J. Schreiber , Maximilian J. Kramer , Alexander Nietner , Jens Eisert

Let $\Phi$ be a uniformly random $k$-SAT formula with $n$ variables and $m$ clauses. We study the algorithmic task of finding a satisfying assignment of $\Phi$. It is known that satisfying assignments exist with high probability up to…

Computational Complexity · Computer Science 2021-11-02 Guy Bresler , Brice Huang