Related papers: Supercritical Space-Width Trade-offs for Resolutio…
As a natural extension of the SAT problem, an array of proof systems for quantified Boolean formulas (QBF) have been proposed, many of which extend a propositional proof system to handle universal quantification. By formalising the…
We examine the $C^{0}$-formulation of the strong cosmic censorship conjecture (SCC) from a quantum complexity-theoretic perspective and argue that for generic black hole parameters as initial conditions for the Einstein equations,…
We prove near-optimal trade-offs for quantifier depth versus number of variables in first-order logic by exhibiting pairs of $n$-element structures that can be distinguished by a $k$-variable first-order sentence but where every such…
Dimensional reduction has proven to be a surprisingly powerful tool for delineating the boundary between the string landscape and the swampland. Bounds from the Weak Gravity Conjecture and the Repulsive Force Conjecture, for instance, are…
We derive an upper bound on the number of models for exact satisfiability (XSAT) of arbitrary CNF formulas F. The bound can be calculated solely from the distribution of positive and negated literals in the formula. For certain subsets of…
We investigate query-to-communication lifting theorems for models related to the quantum adversary bounds. Our results are as follows: 1. We show that the classical adversary bound lifts to a lower bound on randomized communication…
We investigate the size complexity of proofs in $Res(s)$ -- an extension of Resolution working on $s$-DNFs instead of clauses -- for families of contradictions given in the {\em unusual binary} encoding. A motivation of our work is size…
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 consider the mass-subcritical NLS in dimensions $d\geq 3$ with radial initial data. In the defocusing case, we prove that any solution that remains bounded in the critical Sobolev space throughout its lifespan must be global and scatter.…
We investigate the space complexity of refuting $3$-CNFs in Resolution and algebraic systems. We prove that every Polynomial Calculus with Resolution refutation of a random $3$-CNF $\phi$ in $n$ variables requires, with high probability,…
Counterfactual Explanations are becoming a de-facto standard in post-hoc interpretable machine learning. For a given classifier and an instance classified in an undesired class, its counterfactual explanation corresponds to small…
Strong cosmic censorship conjecture has been one of the most important leap of faith in the context of general relativity, providing assurance in the deterministic nature of the associated field equations. Though it holds well for…
The parametrization theorem is derived in a flat nD pseudo-complex affine space. The pseudo-complex hyperbolic space accomodates n-number of uncompactified time-like extra dimensions with sugnature (s,r), where s and r are the numbers of…
We exhibit families of $4$-CNF formulas over $n$ variables that have sums-of-squares (SOS) proofs of unsatisfiability of degree (a.k.a. rank) $d$ but require SOS proofs of size $n^{\Omega(d)}$ for values of $d = d(n)$ from constant all the…
Itsykson and Sokolov [IS14] identified resolution over parities, denoted by $\text{Res}(\oplus)$, as a natural and simple fragment of $\text{AC}^0[2]$-Frege for which no super-polynomial lower bounds on size of proofs are known. Building on…
Already in $\bf{R}^4$, there are many known examples of minimal hypersurfaces, yet few structural results. We show that minimal submanifolds, of any dimension, that are confined in space are very restricted. It is well-known that the…
This paper discusses the topic of the minimum width of a regular resolution refutation of a set of clauses. The main result shows that there are examples having small regular resolution refutations, for which any regular refutation must…
We establish a Trudinger-Moser type inequality with a Tintarev-type constraint in fractional-dimensional spaces and prove the existence of maximizers in the critical regime. Our results provide a refinement of those in (Calc. Var. 52…
Resolution over linear equations is a natural extension of the popular resolution refutation system, augmented with the ability to carry out basic counting. Denoted Res(lin_R), this refutation system operates with disjunctions of linear…
We investigate the space complexity of refuting $3$-CNFs in Resolution and algebraic systems. No lower bound for refuting any family of $3$-CNFs was previously known for the total space in resolution or for the monomial space in algebraic…