An Embryonics Implementation of a Self-Replicating Universal Turing Machine

2001 ◽  
pp. 74-87 ◽  
Author(s):  
Hector Fabio Restrepo ◽  
Daniel Mange
Keyword(s):  
Turing Machine ◽  
Universal Turing Machine

scholarly journals Undecidability in quantum thermalization

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Naoto Shiraishi ◽  
Keiji Matsumoto
Keyword(s):  
Turing Machine ◽  
Thermal Equilibrium ◽  
General Theorem ◽  
Nearest Neighbour ◽  
Many Body ◽  
Initial State ◽  
One Dimensional ◽  
Universal Turing Machine ◽  
Many Body Systems ◽  
Neighbour Interaction

AbstractThe investigation of thermalization in isolated quantum many-body systems has a long history, dating back to the time of developing statistical mechanics. Most quantum many-body systems in nature are considered to thermalize, while some never achieve thermal equilibrium. The central problem is to clarify whether a given system thermalizes, which has been addressed previously, but not resolved. Here, we show that this problem is undecidable. The resulting undecidability even applies when the system is restricted to one-dimensional shift-invariant systems with nearest-neighbour interaction, and the initial state is a fixed product state. We construct a family of Hamiltonians encoding dynamics of a reversible universal Turing machine, where the fate of a relaxation process changes considerably depending on whether the Turing machine halts. Our result indicates that there is no general theorem, algorithm, or systematic procedure determining the presence or absence of thermalization in any given Hamiltonian.

Interactive Computation and Artificial Epistemologies

2021 ◽  
pp. 026327642110485
Author(s):  
Luciana Parisi
Keyword(s):  
Turing Machine ◽  
Mathematical Formalism ◽  
Symbolic Logic ◽  
Formal Models ◽  
Universal Turing Machine ◽  
Interactive Computation

What is algorithmic thought? It is not possible to address this question without first reflecting on how the Universal Turing Machine transformed symbolic logic and brought to a halt the universality of mathematical formalism and the biocentric speciation of thought. The article draws on Sylvia Wynter’s discussion of the sociogenic principle to argue that both neurocognitive and formal models of automated cognition constitute the epistemological explanations of the origin of the human and of human sapience. Wynter’s argument will be related to Gilbert Simondon’s reflections on ‘technical mentality’ to consider how socio-techno-genic assemblages can challenge the biocentricism and the formalism of modern epistemology. This article turns to ludic logic as one possible example of techno-semiotic languages as a speculative overturning of sociogenic programming. Algorithmic rules become technique-signs coinciding not with classic formalism but with interactive localities without re-originating the universality of colonial and patriarchal cosmogony.

Solvable and Unsolvable Problems (1954)

2004 ◽  
Author(s):  
Alan Turing
Keyword(s):  
Turing Machine ◽  
Popular Science ◽  
Systematic Method ◽  
Starting Position ◽  
Universal Turing Machine ◽  
Science News ◽  
Mathematical Problems ◽  
Substitution Type ◽  
Sharpened Form ◽  
Unsolvable Problems

In Chapter 1 Turing proves the existence of mathematical problems that cannot be solved by the universal Turing machine. There he also advances the thesis, now called the Church–Turing thesis, that any systematic method for solving mathematical problems can be carried out by the universal Turing machine. Combining these two propositions yields the result that there are mathematical problems which cannot be solved by any systematic method—cannot, in other words, be solved by any algorithm. In ‘Solvable and Unsolvable Problems’ Turing sets out to explain this result to a lay audience. The article first appeared in Science News, a popular science journal of the time. Starting from concrete examples of problems that do admit of algorithmic solution, Turing works his way towards an example of a problem that is not solvable by any systematic method. Loosely put, this is the problem of sorting puzzles into those that will ‘come out’ and those that will not. Turing gives an elegant argument showing that a sharpened form of this problem is not solvable by means of a systematic method (pp. 591–2). The sharpened form of the problem involves what Turing calls ‘the substitution type of puzzle’. An typical example of a substitution puzzle is this. Starting with the word BOB, is it possible to produce BOOOB by replacing selected occurrences of the pair OB by BOOB and selected occurences of the triple BOB by O? The answer is yes: . . . BOB → BBOOB → BBOBOOB → BOOOB . . .Turing suggests that any puzzle can be re-expressed as a substitution puzzle. Some row of letters can always be used to represent the ‘starting position’ envisaged in a particular puzzle, e.g. in the case of a chess problem, the pieces on the board and their positions. Desired outcomes, for example board positions that count as wins, can be described by further rows of letters, and the rules of the puzzle, whatever they are, are to be represented in terms of permissible substitutions of groups of letters for other groups of letters.

Beyond the universal Turing machine

1999 ◽  
Vol 77 (1) ◽  
pp. 46-66 ◽  
Author(s):  
B. Jack Copeland ◽  
Richard Sylvan
Keyword(s):  
Turing Machine ◽  
Universal Turing Machine

Quantum theory, the Church–Turing principle and the universal quantum computer

1985 ◽  
Vol 400 (1818) ◽  
pp. 97-117 ◽  
Keyword(s):  
Quantum Theory ◽  
Complexity Theory ◽  
Turing Machine ◽  
Physical System ◽  
Quantum Computer ◽  
Physical Principle ◽  
Universal Turing Machine ◽  
Universal Quantum ◽  
Computing Machines ◽  
The Church

It is argued that underlying the Church–Turing hypothesis there is an implicit physical assertion. Here, this assertion is presented explicitly as a physical principle: ‘every finitely realizible physical system can be perfectly simulated by a universal model computing machine operating by finite means’. Classical physics and the universal Turing machine, because the former is continuous and the latter discrete, do not obey the principle, at least in the strong form above. A class of model computing machines that is the quantum generalization of the class of Turing machines is described, and it is shown that quantum theory and the 'universal quantum computer’ are compatible with the principle. Computing machines resembling the universal quantum computer could, in principle, be built and would have many remarkable properties not reproducible by any Turing machine. These do not include the computation of non-recursive functions, but they do include ‘quantum parallelism’, a method by which certain probabilistic tasks can be performed faster by a universal quantum computer than by any classical restriction of it. The intuitive explanation of these properties places an intolerable strain on all interpretations of quantum theory other than Everett’s. Some of the numerous connections between the quantum theory of computation and the rest of physics are explored. Quantum complexity theory allows a physically more reasonable definition of the ‘complexity’ or ‘knowledge’ in a physical system than does classical complexity theory.

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