Related papers: An Invitation to Universality in Physics, Computer…
Turing machines and spin models share a notion of universality according to which some simulate all others. Is there a theory of universality that captures this notion? We set up a categorical framework for universality which includes as…
The paper puts into discussion the concept of universality, in particular for structures not of the power of Turing computability. The question arises if for such structures a universal structure of the same kind exists or not. For that the…
Models of computation operating over the real numbers and computing a larger class of functions compared to the class of general recursive functions invariably introduce a non-finite element of infinite information encoded in an arbitrary…
Many different definitions of computational universality for various types of dynamical systems have flourished since Turing's work. We propose a general definition of universality that applies to arbitrary discrete time symbolic dynamical…
Deutsch, Feynman, and Manin viewed quantum computing as a kind of universal physical simulation procedure. Much of the writing about quantum Turing machines has shown how these machines can simulate an arbitrary unitary transformation on a…
The Turing machine is one of the simple abstract computational devices that can be used to investigate the limits of computability. In this paper, they are considered from several points of view that emphasize the importance and the…
Expanding upon the widely recognized notion of mathematical universality in Turing machines, a concept of thermodynamic universality in Turing machines is introduced. Under the physical Church-Turing thesis, the existence of a…
Turing computability is the standard computability paradigm which captures the computational power of digital computers. To understand whether one can create physically realistic devices which have super-Turing power, one needs to…
Manin, Feynman, and Deutsch have viewed quantum computing as a kind of universal physical simulation procedure. Much of the writing about quantum logic circuits and quantum Turing machines has shown how these machines can simulate an…
Spin models are used in many studies of complex systems---be it condensed matter physics, neural networks, or economics---as they exhibit rich macroscopic behaviour despite their microscopic simplicity. Here we prove that all the physics of…
The theory of spin models intersects with condensed matter physics, complex systems, graph theory, combinatorial optimization, computational complexity and neural networks. Many ensuing applications rely on the fact that complicated spin…
Universal memcomputing machines (UMMs) [IEEE Trans. Neural Netw. Learn. Syst. 26, 2702 (2015)] represent a novel computational model in which memory (time non-locality) accomplishes both tasks of storing and processing of information. UMMs…
One of the theoretical pillars that sustain certain machine learning models are universal approximation theorems, which prove that they can approximate all functions from a function class to arbitrary precision. Independently, classical…
Universality is one of the most important ideas in computability theory. There are various criteria of simplicity for universal Turing machines. Probably the most popular one is to count the number of states/symbols. This criterion is more…
Quantum measurement is universal for quantum computation. This universality allows alternative schemes to the traditional three-step organisation of quantum computation: initial state preparation, unitary transformation, measurement. In…
We construct a two-dimensional Turing machine that is physically universal in both the moving tape and moving head model. In particular, it is mixing of all finite orders in both models. We also provide a variant that is physically…
Quantum measurement is universal for quantum computation. This universality allows alternative schemes to the traditional three-step organisation of quantum computation: initial state preparation, unitary transformation, measurement. In…
When can a model of a physical system be regarded as computable? We provide the definition of a computable physical model to answer this question. The connection between our definition and Kreisel's notion of a mechanistic theory is…
For over a decade, the hypercomputation movement has produced computational models that in theory solve the algorithmically unsolvable, but they are not physically realizable according to currently accepted physical theories. While…
In the present paper, we construct what we call a pedagogical universal Turing machine. We try to understand which comparisons with biological phenomena can be deduced from its encoding and from its working.