Related papers: The normalized algorithmic information distance ca…
It is proved that one cannot approximate stably the first derivative of a smooth function given noisy values of this function and a bound on this function and its first derivative. Such an approximation is shown to be possible if an a…
Sliced Wasserstein distances preserve properties of classic Wasserstein distances while being more scalable for computation and estimation in high dimensions. The goal of this work is to quantify this scalability from three key aspects: (i)…
While Kolmogorov complexity is the accepted absolute measure of information content in an individual finite object, a similarly absolute notion is needed for the information distance between two individual objects, for example, two…
In coding and information theory, it is desirable to construct maximal codes that can be either variable length codes or error control codes of fixed length. However deciding code maximality boils down to deciding whether a given NFA is…
We consider the notion of information distance between two objects x and y introduced by Bennett, G\'acs, Li, Vitanyi, and Zurek [1] as the minimal length of a program that computes x from y as well as computing y from x, and study…
We study the limit computability of finding a global optimum of a continuous function. We give a short proof to show that the problem of checking whether a point is a global minimum is not limit computable. Thereby showing the same for the…
If the no-signalling principle was the only limit to the strength of non-local correlations, we would expect that any form of no-signalling correlation can indeed be realized. That is, there exists a state and measurements that remote…
We comment on recent results in the field of information based complexity, which state (in a number of different settings), that approximation of infinitely differentiable functions is intractable and suffers from the curse of…
An information-theoretic development is given for the problem of compound Poisson approximation, which parallels earlier treatments for Gaussian and Poisson approximation. Let $P_{S_n}$ be the distribution of a sum $S_n=\Sumn Y_i$ of…
We develop quantitative algorithmic information bounds for orthogonal projections and distances in the plane. Under mild independence conditions, the distance $|x-y|$ and a projection coordinate $p_e x$ each retain at least half the…
A data processing inequality states that the quantity of shared information between two entities (e.g. signals, strings) cannot be significantly increased when one of the entities is processed by certain kinds of transformations. In this…
The (Non-Preemptive) Throughput Maximization problem is a natural and fundamental scheduling problem. We are given $n$ jobs, where each job $j$ is characterized by a processing time and a time window, contained in a global interval $[0,T)$,…
This paper concerns algorithms that give correct answers with (asymptotic) density $1$. A dense description of a function $g : \omega \to \omega$ is a partial function $f$ on $\omega$ such that $\left\{n : f(n) = g(n)\right\}$ has density…
We revisit a fundamental problem in string matching: given a pattern of length m and a text of length n, both over an alphabet of size $\sigma$, compute the Hamming distance between the pattern and the text at every location. Several…
Every known communication problem whose randomized communication cost is constant (independent of the input size) can be reduced to $k$-Hamming Distance, that is, solved with a constant number of deterministic queries to some $k$-Hamming…
We propose a fast algorithm to approximate the optimal transport distance. The main idea is to add a Fisher information regularization into the dynamical setting of the problem, originated by Benamou and Brenier. The regularized problem is…
This paper considers the problem of minimizing the ordered weighted average (or ordered median) function of finitely many rational functions over compact semi-algebraic sets. Ordered weighted averages of rational functions are not, in…
The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…
We show that in the case of unknown {\em harmonic oscillator coherent states} it is possible to achieve what we call {\it perfect information cloning}. By this we mean that it is still possible to make arbitrary number of copies of a state…
The celebrated universal approximation theorems for neural networks roughly state that any reasonable function can be arbitrarily well-approximated by a network whose parameters are appropriately chosen real numbers. This paper examines the…