Related papers: Approximate Model Counting: Is SAT Oracle More Pow…
One approach to probabilistic inference involves counting the number of models of a given Boolean formula. Here, we are interested in inferences involving higher-order objects, i.e., functions. We study the following task: Given a Boolean…
Minimal models of a Boolean formula play a pivotal role in various reasoning tasks. While previous research has primarily focused on qualitative analysis over minimal models; our study concentrates on the quantitative aspect, specifically…
We prove a query complexity lower bound for $\mathsf{QMA}$ protocols that solve approximate counting: estimating the size of a set given a membership oracle. This gives rise to an oracle $A$ such that $\mathsf{SBP}^A \not\subset…
Approximate model counting is the task of approximating the number of solutions to an input Boolean formula. The state-of-the-art approximate model counter for formulas in conjunctive normal form (CNF), ApproxMC, provides a scalable means…
Model counting is the task of computing the number of assignments to variables V that satisfy a given propositional theory F. Model counting is an essential tool in probabilistic reasoning. In this paper, we introduce the problem of model…
The analysis discussed in this paper is based on a well-known NP-complete problem which is called satisfiability problem or SAT. From SAT a new NP-complete problem is derived, which is described by a Boolean function called core function.…
Boolean optimization finds a wide range of application domains, that motivated a number of different organizations of Boolean optimizers since the mid 90s. Some of the most successful approaches are based on iterative calls to an NP oracle,…
Hashing-based model counting has emerged as a promising approach for large-scale probabilistic inference on graphical models. A key component of these techniques is the use of xor-based 2-universal hash functions that operate over Boolean…
Model counting ($\#\text{SAT}$) is a fundamental yet $\#\text{P}$-complete problem central to probabilistic reasoning. In this work, we address \textit{incremental model counting}, where sequences of structurally similar formulas must be…
We have focused on Answer Set Programming (ASP), more specifically, answer set counting, exploring both exact and approximate methodologies. We developed an exact ASP counter, sharpASP, which utilizes a compact encoding for propositional…
Propositional model counting, or #SAT, is the problem of computing the number of satisfying assignments of a Boolean formula. Many problems from different application areas, including many discrete probabilistic inference problems, can be…
In this paper, we introduce a general framework for fine-grained reductions of approximate counting problems to their decision versions. (Thus we use an oracle that decides whether any witness exists to multiplicatively approximate the…
In the field of Boolean satisfiability problems (SAT), at-most-k constraints, which suppress the number of true target variables at most k, are often used to describe objective problems. At-most-k constraints are used not only for…
We consider the problem of actively learning an unknown binary decision tree using only membership queries, a setting in which the learner must reason about a large hypothesis space while maintaining formal guarantees. Rather than…
Automated reasoners, such as SAT/SMT solvers and first-order provers, are becoming the backbones of rigorous systems engineering, being used for example in applications of system verification, program synthesis, and cybersecurity.…
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…
This paper proposes a novel approach to determining the internal parameters of the hashing-based approximate model counting algorithm $\mathsf{ApproxMC}$. In this problem, the chosen parameter values must ensure that $\mathsf{ApproxMC}$ is…
In various scenarios, a single phase of modelling and solving is either not sufficient or not feasible to solve the problem at hand. A standard approach to solving AI planning problems, for example, is to incrementally extend the planning…
The computational equivalence between approximate counting and sampling is well established for polynomial-time algorithms. The most efficient general reduction from counting to sampling is achieved via simulated annealing, where the…
Many recent algorithms for approximate model counting are based on a reduction to combinatorial searches over random subsets of the space defined by parity or XOR constraints. Long parity constraints (involving many variables) provide…