Related papers: Computing with and without arbitrary large numbers
Traditional computers work with finite numbers. Situations where the usage of infinite or infinitesimal quantities is required are studied mainly theoretically. In this paper, a recently introduced computational methodology (that is not…
The field of computational complexity is concerned both with the intrinsic hardness of computational problems and with the efficiency of algorithms to solve them. Given such a problem, normally one designs an algorithm to solve it and sets…
We consider a generalisation of the classical Lehmer problem about the parity distribution of an integer and its modular inverse. We use some known estimates of exponential sums to study a more general question of simultaneous distribution…
An indispensable part of our lives, computing has also become essential to industries and governments. Steady improvements in computer hardware have been supported by periodic doubling of transistor densities in integrated circuits over the…
We develop a new intermediate weak memory model, IMM, as a way of modularizing the proofs of correctness of compilation from concurrent programming languages with weak memory consistency semantics to mainstream multi-core architectures,…
GEneral Matrix Multiply (GEMM) is a central operation in deep learning and corresponds to the largest chunk of the compute footprint. Therefore, improving its efficiency is an active topic of ongoing research. A popular strategy is the use…
This paper presents a new representation of natural numbers and discusses its consequences for computability and computational complexity. The paper argues that the introduction of the first Peano axiom in the traditional definition of…
A number of generalizations of stochastic and information-theoretic randomness are known in the literature. However, they are not compatible with handling meaning in vague and dynamic contexts of rough reasoning (and therefore explainable…
Quantum computer algorithms can exploit the structure of random satisfiability problems. This paper extends a previous empirical evaluation of such an algorithm and gives an approximate asymptotic analysis accounting for both the average…
We study approximation and integration problems and compare the quality of optimal information with the quality of random information. For some problems random information is almost optimal and for some other problems random information is…
It is known that quantum computers yield a speed-up for certain discrete problems. Here we want to know whether quantum computers are useful for continuous problems. We study the computation of the integral of functions from the classical…
We examine the characteristic features of reversible and quantum computations in the presence of supplementary external information, known as advice. In particular, we present a simple, algebraic characterization of languages recognized by…
BSS RAMs over first-order structures help to characterize algorithms for processing objects by means of useful operations and relations. They are the result of a generalization of several types of abstract machines. We want to discuss…
Over the past thirty years, there has been significant progress in developing general-purpose, language-based approaches to incremental computation, which aims to efficiently update the result of a computation when an input is changed. A…
We comment on some conceptual and and technical problems related to computational mechanics, point out some errors in several papers, and straighten out some wrong priority claims. We present explicitly the correct algorithm for…
We propose a new type of approximate counting algorithms for the problems of enumerating the number of independent sets and proper colorings in low degree graphs with large girth. Our algorithms are not based on a commonly used Markov chain…
It is folklore particularly in numerical and computer sciences that, instead of solving some general problem f:A->B, additional structural information about the input x in A (that is any kind of promise that x belongs to a certain subset A'…
We start by an introduction to the basic concepts of computability theory and the introduction of the concept of Turing machine and computation universality. Then se turn to the exploration of trade-offs between different measures of…
A coarse description of a subset A of omega is a subset D of omega such that the symmetric difference of A and D has asymptotic density 0. We study the extent to which noncomputable information can be effectively recovered from all coarse…
The Lovasz Local Lemma due to Erdos and Lovasz is a powerful tool in proving the existence of rare events. We present an extension of this lemma, which works well when the event to be shown to exist is a conjunction of individual events,…