Related papers: Counting solutions to random CNF formulas

Given n elements with nonnegative integer weights w1,..., wn and an integer capacity C, we consider the counting version of the classic knapsack problem: find the number of distinct subsets whose weights add up to at most the given…

In the last 30 years it was found that many combinatorial systems undergo phase transitions. One of the most important examples of these can be found among the random k-satisfiability problems (often referred to as k-SAT), asking whether…

Recent formal approaches towards causality have made the concept ready for incorporation into the technical world. However, causality reasoning is computationally hard; and no general algorithmic approach exists that efficiently infers the…

We propose a new type of approximate counting algorithms for the problems of enumerating the number of independent sets and proper colorings in low degree graphs with large girth. Our algorithms are not based on a commonly used Markov chain…

We consider random systems of linear equations over GF(2) in which every equation binds k variables. We obtain a precise description of the clustering of solutions in such systems. In particular, we prove that with probability that tends to…

We propose a novel modular debiasing technique applicable to any discrete random source, addressing the fundamental challenge of reliably extracting high-quality randomness from inherently imperfect physical processes. The method involves…

We determine the exact threshold of satisfiability for random instances of a particular NP-complete constraint satisfaction problem (CSP). This is the first random CSP model for which we have determined a precise linear satisfiability…

Given a Boolean formula $\phi(x)$ in conjunctive normal form (CNF), the density of states counts the number of variable assignments that violate exactly $e$ clauses, for all values of $e$. Thus, the density of states is a histogram of the…

Sample average approximation (SAA) is a tractable approach for dealing with chance constrained programming, a challenging stochastic optimization problem. The constraint of SAA is characterized by the $0/1$ loss function which results in…

We review the connection between statistical mechanics and the analysis of random optimization problems, with particular emphasis on the random k-SAT problem. We discuss and characterize the different phase transitions that are met in these…

The random $k$-XORSAT problem is a random constraint satisfaction problem of $n$ Boolean variables and $m=rn$ clauses, which a random instance can be expressed as a $G\mathbb{F}(2)$ linear system of the form $Ax=b$, where $A$ is a random $m…

Randomized algorithms for deciding satisfiability were shown to be effective in solving problems with thousands of variables. However, these algorithms are not complete. That is, they provide no guarantee that a satisfying assignment, if…

We discuss the implementation of two distributed solvers of the random K-SAT problem, based on some development of the recently introduced survey-propagation (SP) algorithm. The first solver, called the "SP diffusion algorithm", diffuses as…

The estimation of phase transitions in random boolean Constraint Satisfaction Problems (CSP) is based on two fundamental tools: the first and second moment methods. While the first moment method on the number of solutions permits to compute…

We consider the problem of counting the copies of a length-$k$ pattern $\sigma$ in a sequence $f \colon [n] \to \mathbb{R}$, where a copy is a subset of indices $i_1 < \ldots < i_k \in [n]$ such that $f(i_j) < f(i_\ell)$ if and only if…

Boolean satisfiability problem (SAT) is fundamental to many applications. Existing works have used graph neural networks (GNNs) for (approximate) SAT solving. Typical GNN-based end-to-end SAT solvers predict SAT solutions concurrently. We…

Local consistency techniques such as k-consistency are a key component of specialised solvers for constraint satisfaction problems. In this paper we show that the power of using k-consistency techniques on a constraint satisfaction problem…

Let F be a uniformly distributed random k-SAT formula with n variables and m clauses. Non-rigorous statistical mechanics ideas have inspired a message passing algorithm called Belief Propagation Guided Decimation for finding satisfying…

We propose Differentiable Satisfiability and Differentiable Answer Set Programming (Differentiable SAT/ASP) for multi-model optimization. Models (answer sets or satisfying truth assignments) are sampled using a novel SAT/ASP solving…

In this work, we present a novel technique for GPU-accelerated Boolean satisfiability (SAT) sampling. Unlike conventional sampling algorithms that directly operate on conjunctive normal form (CNF), our method transforms the logical…