Related papers: Satisfiability Thresholds for k-CNF Formula with B…

Given a $k$-CNF formula and an integer $s$, we study algorithms that obtain $s$ solutions to the formula that are maximally dispersed. For $s=2$, the problem of computing the diameter of a $k$-CNF formula was initiated by Creszenzi and…

We present a general method for converting any family of unsatisfiable CNF formulas that is hard for one of the simplest proof systems, tree resolution, into formulas that require large rank in any proof system that manipulates polynomials…

A \emph{covering array} is an $N \times k$ array of elements from a $v$-ary alphabet such that every $N \times t$ subarray contains all $v^t$ tuples from the alphabet of size $t$ at least $\lambda$ times; this is denoted as $\CA_\lambda(N;…

Given a CNF formula $\varphi$ with clauses $C_1, \dots, C_m$ over a set of variables $V$, a truth assignment $\mathbf{a} : V \to \{0, 1\}$ generates a binary sequence $\sigma_\varphi(\mathbf{a})=(C_1(\mathbf{a}), \ldots, C_m(\mathbf{a}))$,…

For $n > 2k \geq 4$ we consider intersecting families $\mathcal F$ consisting of $k$-subsets of $\{1, 2, \ldots, n\}$. Let $\mathcal I(\mathcal F)$ denote the family of all distinct intersections $F \cap F'$, $F \neq F'$ and $F, F'\in…

In this paper we present three different results dealing with the number of $(\leq k)$-facets of a set of points: 1. We give structural properties of sets in the plane that achieve the optimal lower bound $3\binom{k+2}{2}$ of $(\leq…

In the Maxmin E$k$-SAT Reconfiguration problem, we are given a satisfiable $k$-CNF formula $\varphi$ where each clause contains exactly $k$ literals, along with a pair of its satisfying assignments. The objective is transform one satisfying…

Let $\Phi$ be a random $k$-SAT formula in which every variable occurs precisely $d$ times positively and $d$ times negatively. Assuming that $k$ is sufficiently large and that $d$ is slightly below the critical degree where the formula…

We study the satisfiability of randomly generated formulas formed by $M$ clauses of exactly $K$ literals over $N$ Boolean variables. For a given value of $N$ the problem is known to be most difficult with $\alpha=M/N$ close to the…

We investigate determining the exact bounds of the frequencies of conjunctions based on frequent sets. Our scenario is an important special case of some general probabilistic logic problems that are known to be intractable. We show that…

We study the problem of sampling an approximately uniformly random satisfying assignment for atomic constraint satisfaction problems i.e. where each constraint is violated by only one assignment to its variables. Let $p$ denote the maximum…

An and/or tree is usually a binary plane tree, with internal nodes labelled by logical connectives, and with leaves labelled by literals chosen in a fixed set of k variables and their negations. In the present paper, we introduce the first…

Preference restrictions have played a significant role in computational social choice. This paper studies a framework that connects preference restrictions with classical graph search paradigms. We model candidates as vertices of a graph…

Ensuring liveness and safety of autonomous and cyber-physical systems remains a fundamental challenge, particularly when multiple safety constraints are present. This letter advances the theoretical foundations of safety-filter Quadratic…

We show that a randomly chosen 3-CNF formula over n variables with clauses-to-variables ratio at least 4.4898 is, as n grows large, asymptotically almost surely unsatisfiable. The previous best such bound, due to Dubois in 1999, was 4.506.…

Let $\{\alpha\}$ and $\{\beta\}$ be nef cohomology classes of bidegree $(1,\,1)$ on a compact $n$-dimensional K\"ahler manifold $X$ such that the difference of intersection numbers $\{\alpha\}^n - n\,\{\alpha\}^{n-1}.\,\{\beta\}$ is…

In their seminal paper from 2004, Kuhn, Moscibroda, and Wattenhofer (KMW) proved a hardness result for several fundamental graph problems in the LOCAL model: For any (randomized) algorithm, there are input graphs with $n$ nodes and maximum…

The satisfaction probability Pr[$\phi$] := Pr$_{\beta:vars(\phi) \to \{0,1\}}[\beta\models \phi]$ of a propositional formula $\phi$ is the likelihood that a random assignment $\beta$ makes the formula true. We study the complexity of the…

We investigate the possibility of an incentive-compatible (IC, a.k.a. strategy-proof) mechanism for the classification of agents in a network according to their reviews of each other. In the $ \alpha $-classification problem we are…

We investigate connections between SAT (the propositional satisfiability problem) and combinatorics, around the minimum degree (number of occurrences) of variables in various forms of redundancy-free boolean conjunctive normal forms…