Related papers: Bounded-Depth Frege Lower Bounds for Random 3-CNFs…
We develop a mathematically and physically sound definition of the spectrally-hyperviscous Navier-Stokes equations (SHNSE) on general bounded domains \Omega with zero (no-slip) boundary conditions prescribed on \varGamma=\partial\varOmega.…
Let $\phi$ be a 3CNF formula with n variables and m clauses. A simple nonconstructive argument shows that when m is sufficiently large compared to n, most 3CNF formulas are not satisfiable. It is an open question whether there is an…
In this note, we propose a framework for proving computational lower bounds in norm approximation by leveraging a reverse detection--estimation gap. The starting point is a testing problem together with an estimator whose error is…
We review the history and previous literature on radical equations and present the rigorous solution theory for radical equations of depth 2, continuing a previous study of radical equations of depth 1. Radical equations of depth 2 are…
Since the introduction of the Ideal Proof System (IPS) by Grochow and Pitassi (J. ACM 2018), a substantial body of work has established size lower bounds for IPS and its fragments. In particular, Forbes, Shpilka, Tzameret, and Wigderson…
We study Frege proofs using depth-$d$ Boolean formulas for the Tseitin contradiction on $n \times n$ grids. We prove that if each line in the proof is of size $M$ then the number of lines is exponential in $n/(\log M)^{O(d)}$. This…
To any fixed, finite relational structure, $\mathbb{D}$, there is an associated decision problem, CSP$(\mathbb{D})$, which is a restricted version of the constraint satisfaction problem. In [8], the so called "algebraic approach" to the…
We study Frege proofs for the one-to-one graph Pigeon Hole Principle defined on the $n\times n$ grid where $n$ is odd. We are interested in the case where each formula in the proof is a depth $d$ formula in the basis given by $\land$,…
In this work we propose and analyze a simple randomized algorithm to find a satisfiable assignment for a Boolean formula in conjunctive normal form (CNF) having at most 3 literals in every clause. Given a k-CNF formula phi on n variables,…
Normal surface theory, a tool to represent surfaces in a triangulated 3-manifold combinatorially, is ubiquitous in computational 3-manifold theory. In this paper, we investigate a relaxed notion of normal surfaces where we remove the…
Proving complexity lower bounds remains a challenging task: we only know how to prove conditional uniform lower bounds and nonuniform lower bounds in restricted circuit models. Williams (STOC 2010) showed how to derive nonuniform lower…
We determine the thresholds for the number of variables, number of clauses, number of clause intersection pairs and the maximum clause degree of a k-CNF formula that guarantees satisfiability under the assumption that every two clauses…
There are various approaches to exploiting "hidden structure" in instances of hard combinatorial problems to allow faster algorithms than for general unstructured or random instances. For SAT and its counting version #SAT, hidden structure…
We demonstrate a family of propositional formulas in conjunctive normal form so that a formula of size $N$ requires size $2^{\Omega(\sqrt[7]{N/logN})}$ to refute using the tree-like OBDD refutation system of Atserias, Kolaitis and Vardi…
We introduce the problem of finding a satisfying assignment to a CNF formula that must further belong to a prescribed input subspace. Equivalent formulations of the problem include finding a point outside a union of subspaces (the…
We study the complexity of fundamental distributed graph problems in the recently popular setting where information about the input graph is available to the nodes before the start of the computation. We focus on the most common such…
We propose a new Nitsche-type approach for weak enforcement of normal velocity boundary conditions for a Lagrangian discretization of the compressible shock-hydrodynamics equations using high-order finite elements on curved boundaries.…
Counting logics with a bounded number of variables form one of the central concepts in descriptive complexity theory. Although they restrict the number of variables that a formula can contain, the variables can be nested within scopes of…
The low-degree polynomial framework has emerged as a powerful tool for providing evidence of statistical-computational gaps in high-dimensional inference. For detection problems, the standard approach bounds the low-degree advantage through…
Previous work of the second author and Wolf showed that given a set $A\subseteq \mathbb{F}_p^n$ of bounded $\textrm{VC}_2$-dimension, there is a high rank quadratic factor $\mathcal{B}$ of bounded complexity such that $A$ is approximately…