Related papers: Resource bounded Ku\v{c}era-G\'{a}cs Theorems

We propose an exact polynomial algorithm for a resource allocation problem with convex costs and constraints on partial sums of resource consumptions, in the presence of either continuous or integer variables. No assumption of strict…

We study the one-shot distillation of general quantum resources, providing a unified quantitative description of the maximal fidelity achievable in this task, and revealing similarities shared by broad classes of resources. We establish…

Motivated by the growing application of wireless multi-access networks with stringent delay constraints, we investigate the Gaussian multiple access channel (MAC) in the finite blocklength regime. Building upon information spectrum…

We prove reducibility of a class of quasi-periodically forced linear equations of the form \[ \partial_tu-\partial_x\circ (1+a(\omega t, x))u+\mathcal{Q}(\omega t)u=0,\quad x\in\mathbb{T}:=\mathbb{R}/2\pi\mathbb{Z}, \] where $u=u(t,x)$, $a$…

In this paper, we revisit the sequential source coding framework to analyze fundamental performance limitations of discrete-time stochastic control systems subject to feedback data-rate constraints in finite-time horizon. The basis of our…

We study Maxwell's equations in conducting media with perfectly conducting boundary conditions on Lipschitz domains, allowing rough material coefficients and $L^2$-data. Our first contribution is a direct proof of well-posedness of the…

For $G$ a semisimple, simply-connected complex algebraic group and two dominant integral weights $\lambda, \mu$, we consider the dimensions of weight spaces $V_\lambda(\mu)$ of weight $\mu$ in the irreducible, finite-dimensional highest…

Using three examples of sequences over a finite alphabet, we want to draw attention to the fact that these sequences having the minimum critical exponent in a given class of sequences show a large degree of symmetry, i.e., they are G-rich…

We prove that, to each synchronous non-local game $\mathcal{G}=(I,O,\lambda)$ with $|I|=n$ and $|O|=m \geq 3$, there is an associated graph $G_{\lambda}$ for which approximate winning strategies for the game $\mathcal{G}$ and the…

By using of analytical multi-logic expresses in conjunction with non-deterministic Turing machine the proposition was proved that algorithm of deterministic Turing counter machine of polynomial time complexity can be decreased to the…

The Robbins-Siegmund theorem is one of the most important results in stochastic optimization, where it is widely used to prove the convergence of stochastic algorithms. We provide a quantitative version of the theorem, establishing a bound…

The goal of this paper is to survey the history, development and current status of the Return Times Theorem and its many extensions and variations. Let $(X, \mathcal{F}, \mu)$ be a finite measure space and let $T:X \rightarrow X$ be a…

In this work, we propose a new bounded arithmetic theory, denoted $APX_1$, designed to formalize a broad class of probabilistic arguments commonly used in theoretical computer science. Under plausible assumptions, $APX_1$ is strictly weaker…

We describe a general technique that yields the first {\em Statistical Query lower bounds} for a range of fundamental high-dimensional learning problems involving Gaussian distributions. Our main results are for the problems of (1) learning…

The manipulation of quantum "resources" such as entanglement, coherence and magic states lies at the heart of quantum science and technology, empowering potential advantages over classical methods. In practice, a particularly important kind…

Quantum resource theories are a powerful framework to characterize and quantify relevant quantum phenomena and identify processes that optimize their use for different tasks. Here, we define a resource measure for magic, the sought-after…

In the recent breakthrough paper by Barbulescu, Gaudry, Joux and Thom{\'e}, a quasi-polynomial time algorithm (QPA) is proposed for the discrete logarithm problem over finite fields of small characteristic. The time complexity analysis of…

Min-entropy sampling gives a bound on the min-entropy of a randomly chosen subset of a string, given a bound on the min-entropy of the whole string. K\"onig and Renner showed a min-entropy sampling theorem that holds relative to quantum…

The well-known Galvin-Prikry Theorem states that Borel subsets of the Baire space are Ramsey: Given any Borel subset $\mathcal{X}\subseteq [\omega]^{\omega}$, where $[\omega]^{\omega}$ is endowed with the metric topology, each infinite…

We show that under mild assumptions for a problem whose solutions admit a dynamic programming-like recurrence relation, we can still find a solution under additional packing constraints, which need to be satisfied approximately. The number…