相关论文: Approximating the satisfiability threshold for ran…

We give an efficient algorithm to strongly refute \emph{semi-random} instances of all Boolean constraint satisfaction problems. The number of constraints required by our algorithm matches (up to polylogarithmic factors) the best-known…

The problem of identifying the satisfiability threshold of random $3$-SAT formulas has received a lot of attention during the last decades and has inspired the study of other threshold phenomena in random combinatorial structures. The…

This paper investigates the controllability of finite-dimensional linear fractional systems involving an uncertain parameter. We establish new results on the simultaneous and average controllability. In particular, we show that average…

We investigate the phase transition in a non-planar correlated percolation model with long-range dependence, obtained by considering level sets of a Gaussian free field with mass above a given height $h$. The dependence present in the model…

Regular signed SAT is a variant of the well-known satisfiability problem in which the variables can take values in a fixed set V \subset [0,1], and the `literals' have the form "x \le a" or "x \ge a". We answer some open question regarding…

We present an experimental study of density and order fluctuations in the vicinity of the solid-liquid-like transition that occurs in a vibrated quasi-two-dimensional granular system. The two-dimensional projected static and dynamic…

Simultaneous estimation of multiple parameters is required in many practical applications. A lower bound on the variance of simultaneous estimation is given by the quantum Fisher information matrix. This lower bound is, however, not…

Propositional satisfiability (SAT) is one of the most fundamental problems in computer science. The worst-case hardness of SAT lies at the core of computational complexity theory. The average-case analysis of SAT has triggered the…

In this paper we compute the coefficients of the reliability polynomial of a consecutive-$k$-out-of-$n$:$F$ system, in Bernstein basis, using the generalized Pascal coefficients. Based on well-known combinatorial properties of the…

We consider a random system of equations $x_i+x_j=b_{(i,j)} (\text{mod }2)$, $(x_u\in \{0,1\},\, b_{(u,v)}=b_{(v,u)}\in\{0,1\})$, with the pairs $(i,j)$ from $E$, a symmetric subset of $[n]\times [n]$. $E$ is chosen uniformly at random…

We give a nearly linear-time algorithm to approximately sample satisfying assignments in the random $k$-SAT model when the density of the formula scales exponentially with $k$. The best previously known sampling algorithm for the random…

We call a CNF formula linear if any two clauses have at most one variable in common. We show that there exist unsatisfiable linear k-CNF formulas with at most 4k^2 4^k clauses, and on the other hand, any linear k-CNF formula with at most…

We study the large-$N$ limit of adjoint fermion one-matrix models. We find one-cut solutions of the loop equations for the correlators of these models and show that they exhibit third order phase transitions associated with $m$-th order…

We consider Achlioptas processes for k-SAT formulas. We create a semi-random formula with n variables and m clauses, where each clause is a choice, made on-line, between two or more uniformly random clauses. Our goal is to delay the…

Here we present a combinatorial decision problem, inspired by the celebrated quiz show called the countdown, that involves the computation of a given target number T from a set of k randomly chosen integers along with a set of arithmetic…

Random $k$-SAT is the single most intensely studied example of a random constraint satisfaction problem. But despite substantial progress over the past decade, the threshold for the existence of satisfying assignments is not known precisely…

Process capability indices such as $C_{pk}$ are widely used in manufacturing quality control to support supplier qualification and product release decisions based on fixed acceptance thresholds (e.g., $C_{pk} \geq 1.33$). In practice, these…

It is well-known that if a subset A of a finite Abelian group G satisfies a quasirandomness property called uniformity of degree k, then it contains roughly the expected number of arithmetic progressions of length k, that is, the number of…

The threshold behaviour of the K-Satisfiability problem is studied in the framework of the statistical mechanics of random diluted systems. We find that at the transition the entropy is finite and hence that the transition itself is due to…

Consider a random $k$-CNF formula $F_{k}(n, rn)$ with $n$ variables and $rn$ clauses. For every truth assignment $\sigma\in \{0, 1\}^{n}$ and every clause $c=\ell_{1}\vee\cdots\vee\ell_{k}$, let $d=d(\sigma, c)$ be the number of satisfied…