The CNNUC3: an analog I/O 64x64 CNN universal machine chip prototype with 7-bit analog accuracy

This chapter talks about cases of many intellectually complex, socially ubiquitous, and highly significant technological innovations, such as the development of fore and aft rigging for sailing vessels that intensified coastal trade in Europe and later the Caribbean. The majority of the blacksmiths who experimented with plows do remain anonymous, but the contribution of James Small was so striking that he left behind a written record as well as a material object. Small was a blacksmith and cartwright from Berwickshire in southern Scotland, who in 1764 introduced a wheel-less iron plow inspired and provoked by his adjustments to the Rotherham plow patented in 1730 by Joseph Foljambe and Disney Stanytown. What made Small stand out was that he was able to articulate the thinking that underpinned his innovations in design. He defined the plow not as an object but as a function.

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The Universal Machine

10.2307/j.ctv11319j8 ◽

2018 ◽

Author(s):

FRED MOTEN

Keyword(s):

Universal Machine

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The Universal Machine

The Digital Mind ◽

10.7551/mitpress/9780262036030.003.0004 ◽

2017 ◽

Author(s):

Arlindo Oliveira

Keyword(s):

Computer Science ◽

Turing Machine ◽

Universal Machine ◽

Alan Turing ◽

Modern Computer ◽

Basic Concepts ◽

The Church

This chapter covers the development of computing, from its origins, with the analytical engine, to modern computer science. Babbage and Ada Lovelace’s contributions to the science of computing led, in time, to the idea of universal computers, proposed by Alan Turing. These universal computers, proposed by Turing, are conceptual devices that can compute anything that can possibly be computed. The basic concepts created by Turing and Church were further developed to create the edifice of modern computer science and, in particular, the concepts of algorithms, computability, and complexity, covered in this chapter. The chapter ends describing the Church-Turing thesis, which states that anything that can be computed can be computed by a Turing machine.

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CHAITIN’S Ω AS A CONTINUOUS FUNCTION

Journal of Symbolic Logic ◽

10.1017/jsl.2019.60 ◽

2019 ◽

Vol 85 (1) ◽

pp. 486-510

Author(s):

RUPERT HÖLZL ◽

WOLFGANG MERKLE ◽

JOSEPH MILLER ◽

FRANK STEPHAN ◽

LIANG YU

Keyword(s):

Continuous Function ◽

Hausdorff Dimension ◽

Universal Machine ◽

Image Position ◽

Turing Complete ◽

Random Reals

AbstractWe prove that the continuous function${\rm{\hat \Omega }}:2^\omega \to $ that is defined via$X \mapsto \mathop \sum \limits_n 2^{ - K\left( {Xn} \right)} $ for all $X \in {2^\omega }$ is differentiable exactly at the Martin-Löf random reals with the derivative having value 0; that it is nowhere monotonic; and that $\mathop \smallint \nolimits _0^1{\rm{\hat{\Omega }}}\left( X \right)\,{\rm{d}}X$ is a left-c.e. $wtt$-complete real having effective Hausdorff dimension ${1 / 2}$.We further investigate the algorithmic properties of ${\rm{\hat{\Omega }}}$. For example, we show that the maximal value of ${\rm{\hat{\Omega }}}$ must be random, the minimal value must be Turing complete, and that ${\rm{\hat{\Omega }}}\left( X \right) \oplus X{ \ge _T}\emptyset \prime$ for every X. We also obtain some machine-dependent results, including that for every $\varepsilon > 0$, there is a universal machine V such that ${{\rm{\hat{\Omega }}}_V}$ maps every real X having effective Hausdorff dimension greater than ε to a real of effective Hausdorff dimension 0 with the property that $X{ \le _{tt}}{{\rm{\hat{\Omega }}}_V}\left( X \right)$; and that there is a real X and a universal machine V such that ${{\rm{\Omega }}_V}\left( X \right)$ is rational.

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