Pascal’s mechanical calculator and Babbage’s Analytic Engine set the stage for a great deal of modern computing machinery. Modern versions of these concepts were finally realized in von Neumann’s architecture in about 1950. However, the science of computing does not depend on physical implementations of these ideas, but rather on virtual machines—that is, abstractions that perform computations ...

We introduce a new so-called distance complexity measure for Turing machine computations which is sensitive to long-distance transfers of information on the worktape. An important special case of this measure can be interpreted as a kind of buffering complexity which counts the number of necessary block uploads into a virtual buffer on top of the worktape. Thus, the distance measure can be used...

A BSS machine is δ-uniform if it does not use exact tests; such machines are equivalent (modulo parameters) to Type 2 Turing machines. We define a notion of closure related to Turing machines for archimedean fields, and show that such fields admit nontrivial δ-uniformly decidable sets iff they are not Turing closed. Then, the partially ordered set of Turing closed fields is proved isomorphic to...

We consider graph Turing machines, a model of parallel computation on a graph, which provides a natural generalization of several standard computational models, including ordinary Turing machines and cellular automata. In this extended abstract, we give bounds on the computational strength of functions that graph Turing machines can compute. We also begin the study of the relationship between t...

Abstract. It was shown that Artificial Recurrent Neural Networks have the same computing power as Turing machines (cf. [6,8]). A Turing machine can be programmed in a proper high-level language the language of partial recursive functions. In this paper we present the implementation of a compiler that directly translates high-level Turing machine programs to Artificial Recursive Neural Networks....

No computer that had not experienced the world as we humans had could pass a rigorously administered standard Turing Test. This paper will show that the use of `subcognitive ’ questions allows the standard Turing Test to indirectly probe the human subcognitive associative concept network built up over a lifetime of experience with the world. Not only can this probing reveal diŒerences in cognit...

Ordinal computability uses ordinals instead of natural numbers in abstract machines like register or Turing machines. We give an overview of the computational strengths of α-β-machines, where α and β bound the time axis and the space axis of some machine model. The spectrum ranges from classical Turing computability to ∞-∞-computability which corresponds to Gödel’s model of constructible sets. ...

While it goes without saying that computing devices need space and time (spacetime), nothing in Turing’s theory of idealized computation prepares one for the rich nature of a computer’s dependence on the underlying spacetime geometry. Nor does that theory prepare one for the vast array of non-Turing computers (and one computer à la Turing) obtained by painting ordinary Turing machine hardware o...

A new computing model, called the active element machine (AEM), is presented that demonstrates Turing incomputable computation using quantum random input. The AEM deterministically executes a universal Turing machine (UTM) program η with random active element firing patterns. These firing patterns are Turing incomputable when the AEM executes a UTM having an unbounded number of computable steps...

A configuration of a Turing machine is given by a tape content together with a particular state of the machine. Petr Kůrka has conjectured that every Turing machine – when seen as a dynamical system on the space of its configurations – has at least one periodic orbit. In this paper, we provide an explicit counter-example to this conjecture. We also consider counter machines and prove that, in t...