Showing papers on "Turing published in 1978"
Book•
1 Jan 1978
TL;DR: The Meta-Morphogenesis project as mentioned in this paper was inspired by Turing's work and has been used to explain how biological brains made possible the deep mathematical discoveries made millennia ago, long before the development of modern logic, often wrongly assumed to provide foundations for all of mathematics.
Abstract: The book presented deep important connections between Artificial Intelligence and Philosophy, based partly on an argument that both philosophy and science are primarily concerned with identifying and explaining possibilities contrary to a common view that science is primarily concerned with laws. The book attempted to show in principle how the construction, testing and debugging of complex computational models, explaining possibilities in a new way, can illuminate a collection of deep philosophical problems, e.g. about the nature of mind, the nature of representation, the nature of mathematical discovery. However it did not claim that this could be done easily or that the problems would be solved soon. 40 years later many of them have still not been solved, including explaining how biological brains made possible the deep mathematical discoveries made millennia ago, long before the development of modern logic, often wrongly assumed to provide foundations for all of mathematics. Later work on these ideas includes the author's Meta-Morphogenesis project, inspired by Alan Turing's work: http://www.cs.bham.ac.uk/research/projects/cogaff/misc/meta-morphogenesis.html
Originally published in 1978 by Harvester Press, this went out of print. An electronic version was created from a scanned in copy and then extensively edited with corrections, addtional text, and notes, available online as html or pdf, intermittently updated. This pdf version was created on 2019/07/09.
223 citations
TL;DR: It is shown that at the first instability point of the homogeneous state the bifurcating branches aresubcritical, and thus emerge as unstable solutions, and that the general idea of symmetry-breaking is perfectly compatible with the generation of regular morphogenetic patterns.
25 citations
TL;DR: In this article, it was shown that the class of uniform upper bounds on I never has a minimal member; if U I = La[A] n Aw for a admissible or a limit of admissibles, the same holds for nice uniform upper bound on I. The central technique used in proving these theorems consists in this: by trial and error construct a generic sequence approximating the desired object; simultaneously settle definitely on finite pieces of that object; make sure that the guessing settles down to the object determined by the limit of these finite pieces.
Abstract: Let I be a countable jump ideal in 9 = . The central theorem of this paper is: a is a uniform upper bound on I iff a computes the join of an I-exact pair whose double jump a\"1' computes. We may replace \"the join of an I-exact pair\" in the above theorem by \"a weak uniform upper bound on I\". We also answer two minimality questions: the class of uniform upper bounds on I never has a minimal member; if U I = La[A] n Aw for a admissible or a limit of admissibles, the same holds for nice uniform upper bounds. The central technique used in proving these theorems consists in this: by trial and error construct a generic sequence approximating the desired object; simultaneously settle definitely on finite pieces of that object; make sure that the guessing settles down to the object determined by the limit of these finite pieces. Fix recursive pairing and unpairing functions on co, such that x = <(x)0, (x)1>. For f: () w), let (f)x(y) = f(). If F c wWc, f parametrizes A iff be = {(f)XIx E w}. We depart from standard practice and view Turing degrees as equivalence classes on WcW, not 9(cw), under T. This has no importance; the following definitions could be rephrased to apply to Turing degrees as usually defined. All degrees in this paper are Turing degrees. A degree a is a uniform upper bound (u.u.b.) on a class I of degrees iff some f E a parametrizes UI; a is a weak u.u.b. if some f E a parametrizes U I n rw2. I is an ideal if I is downward closed under ? and closed under join. I is a jump ideal iff I is an ideal closed under jump. Where I is an ideal, the pair (b, c) is I-exact iff I = {dld < b & d < c}. Recent results of Shore imply that there is a degree-theoretic definition of the relation: a is a u.u.b. on I, where I is a countable jump ideal; it is obtained by encoding the analytic definition of a u.u.b. into degree-theoretic terms. The central result of this paper provides a more natural degree-theoretic definition of this relation. THEOREM 1. Where I is a countable jump ideal: a is a u.u.b. on I iff there is an Iexact pair (b, c),b v c < aand (b v c) (2) -< ab. The technique used in proving the hard direction ( = ) is then extended to answer further questions about u.u.b.s, some of which were raised in [2]. For Y c {(f)XIxe wo}, f is a subparametrization of -. Let f = fo ? * * fn1 iff for all x, f(x) = fi((x)1) if (x)0 = i < n, f(x) = 0 otherwise. Received May 10, 1981. 'I wish to thank David Posner for an illuminating discussion which led to all these theorems. ? 1983, Association for Symbolic Logic 0022-4812/83/4802-0021 /$02.70
11 citations
TL;DR: It is found that not only the Turing condition shall be satisfied, but also that some other requirements must be fulfilled, so that the competence of differentiation is necessary in order to finish the morphogenesic process.
4 citations
1 Jul 1978
TL;DR: It is shown that the Dyck, linear, standard, and bracketed context-free languages are accepted in real-time by one-way bounded cellular acceptors.
Abstract: : The formal language recognition capabilities of one-dimensional one-way bounded cellular automata are studied. In particular, their relationships to real-time two-way bounded cellular acceptors, real-time iterative acceptors, real-time on-line multitape Turing acceptors, and one-way multihead finite acceptors are investigated. It is shown that the Dyck, linear, standard, and bracketed context-free languages are accepted in real-time by one-way bounded cellular acceptors. (Author)
2 citations
TL;DR: The story from the immediate post-war developments at NPL and the Cambridge and Manchester computers already discussed in Part 1, which was published in Electronics & Power, 1978, 24, pp 827-832 as mentioned in this paper.
Abstract: This article continues the story from the immediate post-war developments at NPL and the Cambridge and Manchester computers already discussed in Part 1, which was published in Electronics & Power, 1978, 24, pp 827–832 It will be remembered that Alan Turing's 1946 design for an Automatic Computing Engine ran into difficulties, not least because the design itself and Turing's personality were incompatible with the other early British computer groups
1 citations
1 Jan 1978
TL;DR: On numerous occasions during the Second World War, members of the German high command had reason to believe that the allies knew the contents of some of their most secret communications, but the one thing they did not suspect was the simple truth: the British were able to systematically decipher their secret codes.
Abstract: On numerous occasions during the Second World War, members of the German high command had reason to believe that the allies knew the contents of some of their most secret communications. Naturally, the Nazi leadership was most eager to locate and eliminate this dangerous leak. They were convinced that the problem was one of treachery. The one thing they did not suspect was the simple truth: the British were able to systematically decipher their secret codes. These codes were based on a special machine, the “Enigma,” which the German experts were convinced produced coded messages that were entirely secure. In fact, a young English mathematician, Alan Turing, had designed a special machine for the purpose of decoding messages enciphered using the Enigma. This is not the appropriate place to speculate on the extent to which the course of history might have been different without Turing’s ingenious device, but it can hardly be doubted that it played an extremely important role.