相关论文: Computability and Complexity over the Product Topo…

The TTE approach to Computable Analysis is the study of so-called representations (encodings for continuous objects such as reals, functions, and sets) with respect to the notions of computability they induce. A rich variety of such…

This article is a fundamental study in computable analysis. In the framework of Type-2 effectivity, TTE, we investigate computability aspects on finite and infinite products of effective topological spaces. For obtaining uniform results we…

Although there is a somewhat standard formalization of computability on countable sets given by Turing machines, the same cannot be said about uncountable sets. Among the approaches to define computability in these sets, order-theoretic…

For any class of operators which transform unary total functions in the set of natural numbers into functions of the same kind, we define what it means for a real function to be uniformly computable or conditionally computable with respect…

One of the fundamental results in computability is the existence of well-defined functions that cannot be computed. In this paper we study the effects of data representation on computability; we show that, while for each possible way of…

This paper investigates second-order representations in the sense of Kawamura and Cook for spaces of integrable functions that regularly show up in analysis. It builds upon prior work about the space of continuous functions on the unit…

computable functions are defined by abstract finite deterministic algorithms on many-sorted algebras. We show that there exist finite universal algebraic specifications that specify uniquely (up to isomorphism) (i) all abstract computable…

Computability on uncountable sets has no standard formalization, unlike that on countable sets, which is given by Turing machines. Some of the approaches to define computability in these sets rely on order-theoretic structures to translate…

While there is a well-established notion of what a computable ordinal is, the question which functions on the countable ordinals ought to be computable has received less attention so far. We propose a notion of computability on the space of…

We give an exposition of Natural Topology (NToP), which highlights its advantages for exact computation. The NToP-definition of the real numbers (and continuous real functions) matches recent expert recommendations for exact real…

This paper introduces a more restrictive notion of feasibility of functionals on Baire space than the established one from second-order complexity theory. Thereby making it possible to consider functions on the natural numbers as running…

In this paper, we investigate the problem of synthesizing computable functions of infinite words over an infinite alphabet (data $\omega$-words). The notion of computability is defined through Turing machines with infinite inputs which can…

Kawamura and Cook specified the least set of information about a continuous function on the unit interval which is needed for fast function evaluation. This paper presents a variation of their result. To make the above statement precise,…

Computational complexity characterizes the usage of spatial and temporal resources by computational processes. In the classical theory of computation, e.g. in the Turing Machine model, computational processes employ only local space and…

In the first of this pair of papers, it was proven that that no physical computer can correctly carry out all computational tasks that can be posed to it. The generality of this result follows from its use of a novel definition of…

We investigate the behavior of functional countability and exponential separability in products and subspaces of topological spaces. We solve a problem of Tkachuk by showing that the product of functionally countable pseudocompact spaces is…

This paper formally proposes a problem about the efficient utilization of the four dimensional space-time. Given a cuboid container, a finite number of rigid cuboid items, and the time length that each item should be continuous baked in the…

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…

Computational complexity is a core theory of computer science, which dictates the degree of difficulty of computation. There are many problems with high complexity that we have to deal, which is especially true for AI. This raises a big…

Generalising slightly the notions of a strict computability model and of a simulation between them, which were elaborated by Longley and Normann, we define canonical computability models over categories and appropriate Set-valued functors…