Related papers: Optimal Coding for Randomized Kolmogorov Complexit…
Romashchenko and Zimand~\cite{rom-zim:c:mutualinfo} have shown that if we partition the set of pairs $(x,y)$ of $n$-bit strings into combinatorial rectangles, then $I(x:y) \geq I(x:y \mid t(x,y)) - O(\log n)$, where $I$ denotes mutual…
This paper defines a new notion of bounded computable randomness for certain classes of sub-computable functions which lack a universal machine. In particular, we define such versions of randomness for primitive recursive functions and for…
In this paper we consider a network of processors aiming at cooperatively solving linear programming problems subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set. We propose a…
This paper studies sequence prediction based on the monotone Kolmogorov complexity Km=-log m, i.e. based on universal deterministic/one-part MDL. m is extremely close to Solomonoff's universal prior M, the latter being an excellent…
Random classical linear codes are widely believed to be hard to decode. While slightly sub-exponential time algorithms exist when the coding rate vanishes sufficiently rapidly, all known algorithms at constant rate require exponential time.…
Nowadays there are several classes of constrained codes intended for different applications. The following two large classes can be distinguished. The first class contains codes with local constraints; for example, the source data must be…
It has been shown that one can design distributed algorithms that are (nearly) singularly optimal, meaning they simultaneously achieve optimal time and message complexity (within polylogarithmic factors), for several fundamental global…
Coded computing has emerged as a promising framework for tackling significant challenges in large-scale distributed computing, including the presence of slow, faulty, or compromised servers. In this approach, each worker node processes a…
Consider a binary string $x$ of length $n$ whose Kolmogorov complexity is $\alpha n$ for some $\alpha<1$. We want to increase the complexity of $x$ by changing a small fraction of bits in $x$. This is always possible: Buhrman, Fortnow,…
Constrained coding is a fundamental field in coding theory that tackles efficient communication through constrained channels. While channels with fixed constraints have a general optimal solution, there is increasing demand for parametric…
In this paper, we consider robust control using randomized algorithms. We extend the existing order statistics distribution theory to the general case in which the distribution of population is not assumed to be continuous and the order…
Kolmogorov (1965) defined the complexity of a string $x$ as the minimal length of a program generating $x$. Obviously this definition depends on the choice of the programming language. Kolmogorov noted that there exist \emph{optimal}…
Polar codes have attracted much recent attention as the first codes with low computational complexity that provably achieve optimal rate-regions for a large class of information-theoretic problems. One significant drawback, however, is that…
For every total recursive time bound $t$, a constant fraction of all compressible (low Kolmogorov complexity) strings is $t$-bounded incompressible (high time-bounded Kolmogorov complexity); there are uncountably many infinite sequences of…
Predicting the runtime complexity of a programming code is an arduous task. In fact, even for humans, it requires a subtle analysis and comprehensive knowledge of algorithms to predict time complexity with high fidelity, given any code. As…
We present a new similarity measure based on information theoretic measures which is superior than Normalized Compression Distance for clustering problems and inherits the useful properties of conditional Kolmogorov complexity. We show that…
The ability to find short representations, i.e. to compress data, is crucial for many intelligent systems. We present a theory of incremental compression showing that arbitrary data strings, that can be described by a set of features, can…
This paper presents lossless prefix codes optimized with respect to a pay-off criterion consisting of a convex combination of maximum codeword length and average codeword length. The optimal codeword lengths obtained are based on a new…
In this paper, we consider a network of processors aiming at cooperatively solving mixed-integer convex programs subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set. We propose a…
Classical versions of Kolmogorov complexity are incomputable. Nevertheless, in 1975 Solovay showed that there are computable functions $f > K+O(1)$ such that for infinitely many strings $\sigma$, $f(\sigma)=K(\sigma)+O(1)$, where $K$…