Related papers: Inverse Intersections for Boolean Satisfiability P…
The Boolean Satisfiability problem (SAT), as the prototypical $\mathsf{NP}$-complete problem, is crucial in both theoretical computer science and practical applications. To address this problem, stochastic local search (SLS) algorithms,…
To check the satisfiability of (non-linear) real arithmetic formulas, modern satisfiability modulo theories (SMT) solving algorithms like NLSAT depend heavily on single cell construction, the task of generalizing a sample point to a…
We present DeepSAT, a novel end-to-end learning framework for the Boolean satisfiability (SAT) problem. Unlike existing solutions trained on random SAT instances with relatively weak supervision, we propose applying the knowledge of the…
Maximum Satisfiability (MaxSAT) is an optimization variant of the Boolean Satisfiability (SAT) problem. In general, MaxSAT algorithms perform a succession of SAT solver calls to reach an optimum solution making extensive use of cardinality…
In 2000, I published a relatively comprehensive study of mappings between propositional satisfiability (SAT) and constraint satisfaction problems (CSPs) [Wal00]. I analysed four different mappings of SAT problems into CSPs, and two of CSPs…
In many physical systems, inputs related by intrinsic system symmetries are mapped to the same output. When inverting such systems, i.e., solving the associated inverse problems, there is no unique solution. This causes fundamental…
Finding a quantum computing method to solve nondeterministic polynomial time (NP)-complete problems is currently of paramount importance in quantum information science. Here an experiment is presented to demonstrate the use of Rydberg atoms…
A Boolean constraint satisfaction instance is a conjunction of constraint applications, where the allowed constraints are drawn from a fixed set B of Boolean functions. We consider the problem of determining whether two given constraint…
The inverse eigenvalue problem of a graph $G$ is the problem of characterizing all lists of eigenvalues of real symmetric matrices whose off-diagonal pattern is prescribed by the adjacencies of $G$. The strong spectral property is a…
The problem of P vs. NP is very serious, and solutions to the problem can help save lives. This article is an attempt at solving the problem using a computer algorithm. It is presented in a fashion that will hopefully allow for easy…
Learning-augmented algorithms are a prominent recent development in beyond worst-case analysis. In this framework, a problem instance is provided with a prediction (``advice'') from a machine-learning oracle, which provides partial…
A fertile area of recent research has demonstrated concrete polynomial time lower bounds for solving natural hard problems on restricted computational models. Among these problems are Satisfiability, Vertex Cover, Hamilton Path, Mod6-SAT,…
The satisfiability threshold for constraint satisfaction problems is that value of the ratio of constraints (or clauses) to variables, above which the probability that a random instance of the problem has a solution is zero in the large…
Boolean satisfiability (SAT) problem is of fundamental importance in computer science and many application domains. For Grover's algorithm, solving the SAT problem requires $\mathcal{O}(\sqrt{2^n})$ queries--where n denotes the number of…
Horn-satisfiability or Horn-SAT is the problem of deciding whether a satisfying assignment exists for a Horn formula, a conjunction of clauses each with at most one positive literal (also known as Horn clauses). It is a well-known…
We prove several decidability and undecidability results for the satisfiability and validity problems for languages that can express solutions to word equations with length constraints. The atomic formulas over this language are equality…
This paper is devoted to the complexity of the Boolean satisfiability problem. We consider a version of this problem, where the Boolean formula is specified in the conjunctive normal form. We prove an unexpected result that the…
Dynamical systems can offer a novel non-Boolean approach to computing. Specifically, the natural minimization of energy in the system is a valuable property for minimizing the objective functions of combinatorial optimization problems, many…
Matrix completion aims to predict missing elements in a partially observed data matrix which in typical applications, such as collaborative filtering, is large and extremely sparsely observed. A standard solution is matrix factorization,…
We investigate connections between SAT (the propositional satisfiability problem) and combinatorics, around the minimum degree (number of occurrences) of variables in various forms of redundancy-free boolean conjunctive normal forms…