Related papers: On low for speed oracles
Computational problems are classified into computable and uncomputable problems. If there exists an effective procedure (algorithm) to compute a problem then the problem is computable otherwise it is uncomputable. Turing machines can…
Low-latency sliding window algorithms for regular and context-free languages are studied, where latency refers to the worst-case time spent for a single window update or query. For every regular language $L$ it is shown that there exists a…
We introduce two notions of effective reducibility for set-theoretical statements, based on computability with Ordinal Turing Machines (OTMs), one of which resembles Turing reducibility while the other is modelled after Weihrauch…
A type-2 computable real function is necessarily continuous; and this remains true for relative, i.e. oracle-based computations. Conversely, by the Weierstrass Approximation Theorem, every continuous f:[0,1]->R is computable relative to…
The search task is one of the most difficult when it comes to execution speed, and reducing the latter is important both when working with large data and with small samples, if they need to be processed frequently and in a limited time.…
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…
The notion of slow provability for Peano Arithmetic ($\mathsf{PA}$) was introduced by S.D. Friedman, M. Rathjen, and A. Weiermann. They studied the slow consistency statement $\mathrm{Con}_{\mathsf{s}}$ that asserts that a contradiction is…
We address the question of computing one selected term of an algebraic power series. In characteristic zero, the best algorithm currently known for computing the $N$th coefficient of an algebraic series uses differential equations and has…
We prove in this paper that there is a language $L_s$ accepted by some nondeterministic Turing machine that runs within time $O(n^k)$ for any positive integer $k\in\mathbb{N}_1$ but not by any ${\rm co}\mathcal{NP}$ machines. Then we…
Reversible forms of computations are often interesting from an energy efficiency point of view. When the computation device in question is an automaton, it is known that the minimal reversible automaton recognizing a given language is not…
We investigate properties of estimators obtained by minimization of U-processes with the Lasso penalty in high-dimensional settings. Our attention is focused on the ranking problem that is popular in machine learning. It is related to…
When a computer algebra system fails to solve an Ordinary Differential Equation, is this a limitation of its implementation, or a genuine computational barrier? Three traditions bear on the question. Modern computer algebra algorithms can…
We study the problem of using low computational cost to automate the choices of learners and hyperparameters for an ad-hoc training dataset and error metric, by conducting trials of different configurations on the given training data. We…
In this paper we have investigated enumeration orders of elements of r.e. sets enumerated by means of Turing machines. We have defined a reducibility based on enumeration orders named "Enumeration Order Reducibility" on computable functions…
Bennett's notion of depth is usually considered to describe the usefulness and internal organization of the information encoded into an object such as an infinite binary sequence. We consider a natural way to relativize the notion of depth…
A remarkable new definition of a self-delimiting universal Turing machine is presented that is easy to program and runs very quickly. This provides a new foundation for algorithmic information theory. This new universal Turing machine is…
Low-cardinality activations permit an algorithm based on fetching the inference values from pre-calculated lookup tables instead of calculating them every time. This algorithm can have extensions, some of which offer abilities beyond those…
We introduce a general approach to prove oracle properties in context tree selection. The results derive from a concentration condition that is verified, for example, by mixing processes. Moreover, we show the superiority of the oracle…
Tabular foundation models are becoming increasingly popular for low-resource tabular problems. These models make up for small training datasets by pretraining on large volumes of synthetic data. The prior knowledge obtained via pretraining…
We pose the following question: If a physical experiment were to be completely controlled by an algorithm, what effect would the algorithm have on the physical measurements made possible by the experiment? In a programme to study the nature…