Turing-like patterns induced by the competition between two stable states in a discrete-time predator–prey model
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Alan Turing, a mathematician, logician, and computer scientist, is widely considered to be the father of computer science. In the 1930s, he invented the Universal Turing Machine. Assuming enough memory is available, the Turing Machine could calculate anything using only two symbols (0 or 1) arranged in a potentially infinite one-dimensional sequence. This is the basis for the first computer. Turing-completeness, therefore, refers to any computation problem that can be solved and implemented in a Turing-complete environment, no matter how complex.
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Abstract Although Turing in his later years became interested in the use of reaction diffusion equations to model morphogenesis (cf. Turing 1952) my task in this essay is to trace the way in which Turing’s notion of the universal computer led to a computational theory of organism growth and reproduction. The focus, then, is on the work in the 1960’s that was spurred by von Neumann’s (1951, 1966) theory of self-reproducing automata. Turing’s result that there exists a universal computing machine suggested to von Neumann that there might be a universal construction machine A, which, when furnished with a suitable description IN of any appropriate automaton N, will construct a copy of N.
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Turing machines are abstract computing devices, named after Alan Mathison Turing. A Turing machine operates on a potentially infinite tape uniformly divided into squares, and is capable of entering only a finite number of distinct internal configurations. Each square may contain a symbol from a finite alphabet. The machine can scan one square at a time and perform, depending on the content of the scanned square and its own internal configuration, one of the following operations: print or erase a symbol on the scanned square or move on to scan either one of the immediately adjacent squares. These elementary operations are possibly accompanied by a change of internal configuration. Turing argued that the class of functions calculable by means of an algorithmic procedure (a mechanical, stepwise, deterministic procedure) is to be identified with the class of functions computable by Turing machines. The epistemological significance of Turing machines and related mathematical results hinges upon this identification, which later became known as Turing’s thesis; an equivalent claim, Church’s thesis, had been advanced independently by Alonzo Church. Most crucially, mathematical results stating that certain functions cannot be computed by any Turing machine are interpreted, by Turing’s thesis, as establishing absolute limitations of computing agents.
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Abstract A body of recent literature has proposed that explanation in neurosciences, including cognitive neuroscience, is mechanistic. It has also been argued that the mechanistic model could be extended to cover explanations in computer sciences and cognitive sciences. Mechanistic explanation as standardly conceived is a form of causal explanation, and it requires that the explanatory mechanisms are concrete, implemented mechanisms. However, ‘computing mechanisms’ can mean two things. On the one hand, it can refer to concrete — causal — computing mechanisms, such as brains (ex hypothesi ) or man‐made computers, etc. On the other hand, it can also refer to abstract computing mechanisms such as abstract Turing machines. Therefore, the notion of computation can be used in cognitive science in at least two ways. Since there are computational explanations, in which Turing machines are considered as abstract mechanisms, the current formulation of mechanistic explanation does not cover those explanations.
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The paper offers a mathematical formalization of the Turing test. This formalization makes it possible to establish the conditions under which some Turing machine will pass the Turing test and the conditions under which every Turing machine (or every Turing machine of the special class) will fail the Turing test.
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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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This paper introduces a new computing model based on the cooperation among Turing machines called orchestrated machines. Like universal Turing machines, orchestrated machines are also designed to simulate Turing machines but they can also modify the original operation of the included Turing machines to create a new layer of some kind of collective behavior. Using this new model we can define some interested notions related to cooperation ability of Turing machines such as the intelligence quotient or the emotional intelligence quotient for Turing machines.
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