Related papers: A Scalable Approximate Model Counter
Propositional satisfiability (SAT) solvers, which typically operate using conjunctive normal form (CNF), have been successfully applied in many domains. However, in some application areas such as circuit verification, bounded model…
The study of phase transition phenomenon of NP complete problems plays an important role in understanding the nature of hard problems. In this paper, we follow this line of research by considering the problem of counting solutions of…
Boolean Satisfiability Problem (SAT) is one of the core problems in computer science. As one of the fundamental NP-complete problems, it can be used - by known reductions - to represent instances of variety of hard decision problems.…
We describe how to use propositional model counting for a quantitative analysis of product configuration data. Our approach computes valuable meta information such as the total number of valid configurations or the relative frequency of…
Model counting is a fundamental problem that consists of determining the number of satisfying assignments for a given Boolean formula. The weighted variant, which computes the weighted sum of satisfying assignments, has extensive…
We study the problem of finding a small subset of items that is \emph{agreeable} to all agents, meaning that all agents value the subset at least as much as its complement. Previous work has shown worst-case bounds, over all instances with…
First-order model counting (FOMC) is the problem of counting the number of models of a sentence in first-order logic. Since lifted inference techniques rely on reductions to variants of FOMC, the design of scalable methods for FOMC has…
Inference-time scaling has recently emerged as a powerful paradigm for improving the reasoning capability of large language models. Among various approaches, Sequential Monte Carlo (SMC) has become a particularly important framework,…
In this paper, we propose an approximating framework for analyzing parametric Markov models. Instead of computing complex rational functions encoding the reachability probability and the reward values of the parametric model, we exploit the…
This paper describes a novel unbounded software model checking approach to find errors in programs written in the C language based on incremental SAT-solving. Instead of using the traditional assumption based API to incremental SAT solvers…
Predictive models are being increasingly used to support consequential decision making at the individual level in contexts such as pretrial bail and loan approval. As a result, there is increasing social and legal pressure to provide…
Over the past several decades, CDCL SAT solvers have proven remarkably effective on large industrial formulas, despite SAT being NP-complete and widely believed to be intractable. While considerable empirical research has been done on…
The class-agnostic counting (CAC) task has recently been proposed to solve the problem of counting all objects of an arbitrary class with several exemplars given in the input image. To address this challenging task, existing leading methods…
Maximizing a single submodular set function subject to a cardinality constraint is a well-studied and central topic in combinatorial optimization. However, finding a set that maximizes multiple functions at the same time is much less…
Parity-SAT is the problem of determining whether a given CNF formula has an odd number of satisfying assignments. As a canonical $\oplus$P-complete problem, it represents a fundamental variant of the exact model counting problem (#SAT).…
As was shown recently, many important AI problems require counting the number of models of propositional formulas. The problem of counting models of such formulas is, according to present knowledge, computationally intractable in a worst…
The task of estimating a matrix given a sample of observed entries is known as the \emph{matrix completion problem}. Most works on matrix completion have focused on recovering an unknown real-valued low-rank matrix from a random sample of…
The Exact Satisfiability problem, XSAT, is defined as the problem of finding a satisfying assignment to a formula in CNF such that there is exactly one literal in each clause assigned to be 1 and the other literals in the same clause are…
The boolean satisfiability (SAT) problem asks whether there exists an assignment of boolean values to the variables of an arbitrary boolean formula making the formula evaluate to True. It is well-known that all NP-problems can be coded as…
We consider the hardness of approximation of optimization problems from the point of view of definability. For many NP-hard optimization problems it is known that, unless P = NP, no polynomial-time algorithm can give an approximate solution…