Related papers: The Incomputable Alan Turing
Optimization problems are a staple of today's scientific and technical landscape. However, at present, solvers of such problems are almost exclusively run on digital hardware. Using Turing machines as a mathematical model for any type of…
Linear logic was conceived in 1987 by Girard and, in contrast to classical logic, restricts the usage of the structural inference rules of weakening and contraction. With this, atoms of the logic are no longer interpreted as truth, but as…
The Turing Test is no longer adequate for distinguishing human and machine intelligence. With advanced artificial intelligence systems already passing the original Turing Test and contributing to serious ethical and environmental concerns,…
A universal Turing machine is a powerful concept - a single device can compute any function that is computable. A universal spin model, similarly, is a class of physical systems whose low energy behavior simulates that of any spin system.…
In this essay, I argue that explicit ethical machines, whose moral principles are inferred through a bottom-up approach, are unable to replicate human-like moral reasoning and cannot be considered moral agents. By utilizing Alan Turing's…
Real-life agents seldom have unlimited reasoning power. In this paper, we propose and study a new formal notion of computationally bounded strategic ability in multi-agent systems. The notion characterizes the ability of a set of agents to…
Una de las presuposiciones de la ciencia desde los tiempos de Galileo, Newton y Laplace ha sido la previsibilidad del mundo. Esta idea ha influido en los modelos cientificos y tecnologicos. Sin embargo, en las ultimas decadas, el caos y la…
This is a typeset version of Alan Turing's declassified Second World War paper \textit{Paper on Statistics of Repetitions}. See the companion paper, \textit{The Applications of Probability to Cryptography}, also available from arXiv at…
So far, following the works of A.M. Turing, the algorithms were considered as the mathematical abstraction from which we could write programs for computers whose principle was based on the theoretical concept of Turing machine. We start…
This book develops the conjecture that all kinds of information processing in computers and in brains may usefully be understood as "information compression by multiple alignment, unification and search". This "SP theory", which has been…
This paper presents a soundness and completeness proof for propositional intuitionistic calculus with respect to the semantics of computability logic. The latter interprets formulas as interactive computational problems, formalized as games…
The Turing Award is recognized as the most influential and prestigious award in the field of computer science(CS). With the rise of the science of science (SciSci), a large amount of bibliographic data has been analyzed in an attempt to…
Manin, Feynman, and Deutsch have viewed quantum computing as a kind of universal physical simulation procedure. Much of the writing about quantum logic circuits and quantum Turing machines has shown how these machines can simulate an…
There is a cognitive limit in Human Mind. This cognitive limit has played a decisive role in almost all fields including computer sciences. The cognitive limit replicated in computer sciences is responsible for inherent Computational…
The upper limit on what is computable in our universe is unknown, but widely believed to be set by the Turing machine -- with a function being physically computable if and only if it is Turing-computable. I show how this apparently mild…
Turing's famous `machine' model constitutes the first intuitively convincing framework for computing with real numbers. Kleene's computation schemes S1-S9 extend Turing's approach to computing with objects of any finite type. Both…
Considering that Turing's original test was co-opted by Weizenbaum and that six of the most common criticisms of the Turing test are unfair to both Turing's argument and the historical development of AI.
Quantum mechanics is a theory that is as effective as it is counterintuitive. While quantum practices operate impeccably, they compel us to embrace enigmatic phenomena like the collapse of the state vector and non-locality, thereby pushing…
This paper delves into the intersection of computational theory and music, examining the concept of undecidability and its significant, yet overlooked, implications within the realm of modern music composition and production. It posits that…
There is much to learn from what Turing hastily dismissed as Lady Lovelace s objection. Digital computers can indeed surprise us. Just like a piece of art, algorithms can be designed in such a way as to lead us to question our understanding…