Related papers: Decomposing Hard SAT Instances with Metaheuristic …
We consider a popular family of constrained optimization problems arising in machine learning that involve optimizing a non-decomposable evaluation metric with a certain thresholded form, while constraining another metric of interest.…
We propose a resource-constrained heuristic for instances of Max-SAT that iteratively decomposes a larger problem into smaller subcomponents that can be solved by optimized solvers and hardware. The unconstrained outer loop maintains the…
As the cornerstone of modern power systems, the Unit Commitment Problem (UC) is critical for ensuring operational security and economic efficiency in the ongoing global energy transition. However, existing UC studies typically propose…
Maximizing a monotone submodular function is a fundamental task in machine learning. In this paper, we study the deletion robust version of the problem under the classic matroids constraint. Here the goal is to extract a small size summary…
The Boolean Satisfiability (SAT) problem stands out as an attractive NP-complete problem in theoretic computer science and plays a central role in a broad spectrum of computing-related applications. Exploiting and tuning SAT solvers under…
In this manuscript, we derive the principle of conservation of computational complexity. We measure computational complexity as the number of binary computations (decisions) required to solve a problem. Every problem then defines a unique…
This paper explores the Boolean Satisfiability Problem (SAT) in the context of Kolmogorov complexity theory. We present three versions of the distinguishability problem-Boolean formulas, Turing machines, and quantum systems-each focused on…
Modern software for propositional satisfiability problems gives a powerful automated reasoning toolkit, capable of outputting not only a satisfiable/unsatisfiable signal but also a justification of unsatisfiability in the form of resolution…
Consider the regularized sparse minimization problem, which involves empirical sums of loss functions for $n$ data points (each of dimension $d$) and a nonconvex sparsity penalty. We prove that finding an…
This paper presents algorithms for the included-sums and excluded-sums problems used by scientific computing applications such as the fast multipole method. These problems are defined in terms of a $d$-dimensional array of $N$ elements and…
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…
Random instances of constraint satisfaction problems such as k-SAT provide challenging benchmarks. If there are m constraints over n variables there is typically a large range of densities r=m/n where solutions are known to exist with…
Understanding properties of deep neural networks is an important challenge in deep learning. In this paper, we take a step in this direction by proposing a rigorous way of verifying properties of a popular class of neural networks,…
The basic random $k$-SAT problem is: Given a set of $n$ Boolean variables, and $m$ clauses of size $k$ picked uniformly at random from the set of all such clauses on our variables, is the conjunction of these clauses satisfiable? Here we…
Bayesian optimization works effectively optimizing parameters in black-box problems. However, this method did not work for high-dimensional parameters in limited trials. Parameters can be efficiently explored by nonlinearly embedding them…
In the present paper, we propose a technology for translating algorithmic descriptions of discrete functions to SAT. The proposed technology is aimed at applications in algebraic cryptanalysis. We describe how cryptanalysis problems are…
This paper formalizes the optimal base problem, presents an algorithm to solve it, and describes its application to the encoding of Pseudo-Boolean constraints to SAT. We demonstrate the impact of integrating our algorithm within the…
While accelerated computing has transformed many domains of computing, its impact on logical reasoning, specifically Boolean satisfiability (SAT), remains limited. State-of-the-art SAT solvers rely heavily on inherently sequential…
Much effort is spent everyday by programmers in trying to reduce long, failing execution traces to the cause of the error. We present a new algorithm for error cause localization based on a reduction to the maximal satisfiability problem…
In this paper we present and evaluate a search strategy called Decomposition Based Search (DBS) which is based on two steps: subproblem generation and subproblem solution. The generation of subproblems is done through value ranking and…