Related papers: Three computational models and its equivalence

To scrutinize notions of computation and time complexity, we introduce and formally define an interactive model for computation that we call it the \emph{computation environment}. A computation environment consists of two main parts: i) a…

A novel computing model, called \emph{Probe Machine}, is proposed in this paper. Different from Turing Machine, Probe Machine is a fully-parallel computing model in the sense that it can simultaneously process multiple pairs of data, rather…

We study a classical realizability model (in the sense of J.-L. Krivine) arising from a model of untyped lambda calculus in coherence spaces. We show that this model validates countable choice using bar recursion and bar induction.

In his seminal paper ``Computing Machinery and Intelligence'', Alan Turing introduced the ``imitation game'' as part of exploring the concept of machine intelligence. The Turing Test has since been the subject of much analysis, debate,…

Computational Logic is the use of computers to establish facts in a logical formalism. Originating in 19th-century attempts to understand the nature of mathematical reasoning, the subject now comprises a wide variety of formalisms,…

Despite ongoing calls for inclusive and culturally responsive pedagogy in computing education, the teaching of algorithms remains largely decontextualized. Foundational computer science courses often present algorithmic thinking as purely…

Reversible computation opens up the possibility of overcoming some of the hardware's current physical limitations. It also offers theoretical insights, as it enriches multiple paradigms and models of computation, and sometimes…

Just as the $\lambda$-calculus uses three primitives (abstraction, application, variable) as the foundation of functional programming, inheritance-calculus uses three primitives (record, definition, inheritance) as the foundation of…

The Church-Turing thesis is one of the pillars of computer science; it postulates that every classical system has equivalent computability power to the so-called Turing machine. While this thesis is crucial for our understanding of…

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…

Recursive analysis was introduced by A. Turing [1936], A. Grzegorczyk [1955], and D. Lacombe [1955]. It is based on a discrete mechanical framework that can be used to model computation over the real numbers. In this context the…

Since the Turing test was first proposed by Alan Turing in 1950, the primary goal of artificial intelligence has been predicated on the ability for computers to imitate human behavior. However, the majority of uses for the computer can be…

I show that the cloneability of information is the key difference between classical computer and quantum computer. As information stored and processed by neurons is cloneable, brain (human or non-human) is a classical computer. Penrose…

The main deficiency of the algorithms running on digital computers nowadays is their inability to change themselves during the execution. In line with this, the paper introduces the so-called replicated algorithms, inspired by the concept…

Although the Turing-machine model of computation is widely used in computer science it is fundamentally inadequate as a foundation for the theory of modern scientific computation. The real-number model is described as an alternative.…

The traditional foundation of science lies on the cornerstones of theory and experiment. Theory is used to explain experiment, which in turn guides the development of theory. Since the advent of computers and the development of…

This paper provides a new and more direct proof of the assertion that a Turing computable function of the natural numbers is primitive recursive if and only if the time complexity of the corresponding Turing machine is bounded by a…

The point of building a quantum computer is that it allows to model living things with predictive power and gives the opportunity to control life. Its scaling means not just the improvement of the instrument part, but also, mainly,…

Consider a universal Turing machine that produces a partial or total function (or a binary stream), based on the answers to the binary queries that it makes during the computation. We study the probability that the machine will produce a…

Charles Babbage's vision of computing has largely been realized. We are on the verge of realizing Vannevar Bush's Memex. But, we are some distance from passing the Turing Test. These three visions and their associated problems have provided…