Many years ago I was invited to give a lecture on what is today called " computer science " at a large eastern university. I titled my lecture " Turing machines " , because the most famous abstract model of a computer is the model presented by Alan Turing. Today biographies of Turing are reviewed in the New York Times, but in those early days of the computer Turing was virtually unheard of. Thu...

i? recent years the need for a rigorous formaliza!ion’hbf the mathematical properties of computer programs has become increasingly evident. Problems in program proving, for exampie, require that a precise meanir!.: be given to otherwise intuitive notions. One such formalization has been suggested by Milner [6] and has been successfully used in areas such as program and machine verification (see...

We obtain the first deterministic randomness extractors for n-bit sources with minentropy ≥ n1−α generated (or sampled) by single-tape Turing machines running in time n2−16α, for all sufficiently small α > 0. We also show that such machines cannot sample a uniform n-bit input to the Inner Product function together with the output. The proofs combine a variant of the crossing-sequence technique ...

Recently, Neural Turing Machine and Memory Networks have shown that adding an external memory can greatly ameliorate a traditional recurrent neural network’s tendency to forget after a long period of time. Here we present a new design of an external memory, wherein memories are stored in an Euclidean key space R. An LSTM controller performs read and write via specialized structures called read ...

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...

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. ...