Related papers: Sub-computable Boundedness Randomness
In this paper we introduce the notion of $e$-computability as a method of finding the Waring rank of forms. We use this notion to find infinitely many new examples which satisfy Strassen's Conjecture.
Reversible computing is motivated by both pragmatic and foundational considerations arising from a variety of disciplines. We take a particular path through the development of reversible computation, emphasizing compositional reversible…
We develop a general framework for extracting highly uniform bounds on local stability for stochastic processes in terms of information on fluctuations or crossings. This includes a large class of martingales: As a corollary of our main…
Several classes of DNR functions are characterized in terms of Kolmogorov complexity. In particular, a set of natural numbers A can wtt-compute a DNR function iff there is a nontrivial recursive lower bound on the Kolmogorov complexity of…
Algorithmic statistics studies explanations of observed data that are good in the algorithmic sense: an explanation should be simple i.e. should have small Kolmogorov complexity and capture all the algorithmically discoverable regularities…
We exhibit a sound and complete implicit-complexity formalism for functions feasibly computable by structural recursions over inductively defined data structures. Feasibly computable here means that the structural-recursive definition runs…
We derive recursions for the probability distribution of random sums by computer algebra. Unlike the well-known Panjer-type recursions, they are of finite order and thus allow for computation in linear time. This efficiency is bought by the…
We investigate partial functions and computability theory from within a constructive, univalent type theory. The focus is on placing computability into a larger mathematical context, rather than on a complete development of computability…
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…
A new definition of random sets is proposed. It is based on the distance in measurable space and uses negative definite kernels for continuation from initial space to that of random sets. This approach has no connection to Hausdorff…
A new characterization of provably recursive functions of first-order arithmetic is described. Its main feature is using only terms consisting of 0, the successor S and variables in the quantifier rules, namely, universal elimination and…
This paper examines the foundational concept of random variables in probability theory and statistical inference, demonstrating that their mathematical definition requires no reference to randomization or hypothetical repeated sampling. We…
In a prequential approach to algorithmic randomness, probabilities for the next outcome can be forecast `on the fly' without the need for fully specifying a probability measure on all possible sequences of outcomes, as is the case in the…
The incompressibility method is a counting argument in the framework of algorithmic complexity that permits discovering properties that are satisfied by most objects of a class. This paper gives a preliminary insight into Kolmogorov's…
Computable reducibility is a well-established notion that allows to compare the complexity of various equivalence relations over the natural numbers. We generalize computable reducibility by introducing degree spectra of reducibility and…
Many theorems about Kolmogorov complexity rely on existence of combinatorial objects with specific properties. Usually the probabilistic method gives such objects with better parameters than explicit constructions do. But the probabilistic…
A Bayesian approach to the classification problem is proposed in which random partitions play a central role. It is argued that the partitioning approach has the capacity to take advantage of a variety of large-scale spatial structures, if…
We study the computational complexity of universality and inclusion problems for unambiguous finite automata and context-free grammars. We observe that several such problems can be reduced to the universality problem for unambiguous…
We survey recent developments in the study of probabilistic complexity classes. While the evidence seems to support the conjecture that probabilism can be deterministically simulated with relatively low overhead, i.e., that $P=BPP$, it also…
The Ku\v{c}era-G\'acs theorem is a landmark result in algorithmic randomness asserting that every real is computable from a Martin-L\"of random real. If the computation of the first $n$ bits of a sequence requires $n+h(n)$ bits of the…