Related papers: A Physically Universal Turing Machine

Turing machines and G\"odel numbers are important pillars of the theory of computation. Thus, any computational architecture needs to show how it could relate to Turing machines and how stable implementations of Turing computation are…

The pseudoinverse of a matrix, a generalized notion of the inverse, is of fundamental importance in linear algebra and, thereby, in many different fields. Despite its proven existence, an algorithmic approach is typically necessary to…

An algebraic representation of the Turing machines is given, where the configurations of Turing machines are represented by 4 order tensors, and the transition functions by 8 order tensors. Two types of tensor product are defined, one is to…

Using nonstandard analysis, we will extend the classical Turing machines into the internal Turing machines. The internal Turing machines have the capability to work with infinite ($*$-finite) number of bits while keeping the finite…

The idea behind universal coating is to have a thin layer of a specific substance covering an object of any shape so that one can measure a certain condition (like temperature or cracks) at any spot on the surface of the object without…

Infinite time Turing machines extend the operation of ordinary Turing machines into transfinite ordinal time. By doing so, they provide a natural model of infinitary computability, a theoretical setting for the analysis of the power and…

If every vertex in a map has one out of two face-cycle types, then the map is said to be $2$-semiequivelar. A 2-uniform tiling is an edge-to-edge tiling of regular polygons having $2$ distinct transitivity classes of vertices. Clearly, a…

Finite Turing computation has a fundamental symmetry between inputs, outputs, programs, time, and storage space. Standard models of transfinite computational break this symmetry; we consider ways to recover it and study the resulting model…

Several machine learning models are defined for inputs of any size, such as graphs with different numbers of nodes and point clouds containing varying numbers of points. The universality properties of such any-dimensional models remain…

Foundations of the theory of quantum Turing machines are investigated. The protocol for the preparation and the measurement of quantum Turing machines is discussed. The local transition functions are characterized for fully general quantum…

Efforts at understanding the computational processes in the brain have met with limited success, despite their importance and potential uses in building intelligent machines. We propose a simple new model which draws on recent findings in…

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…

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…

A novel computing model, called \emph{Probe Machine}, is proposed in this paper. Different from Turing Machine, Probe Machine is a fully-parallel computing model in the sense that it can simultaneously process multiple pairs of data, rather…

Topological classification of the 4-manifolds bridges computation theory and physics. A proof of the undecidability of the homeomorphy problem for 4-manifolds is outlined here in a clarifying way. It is shown that an arbitrary Turing…

It is proved that a quantum computer with fixed and permanent interaction of diagonal type between qubits proposed in the work quant-ph/0201132 is universal. Such computer is controlled only by one-qubit quick transformations, and this…

In this paper we investigate the computational power of a set of mobile robots with limited visibility. At each iteration, a robot takes a snapshot of its surroundings, uses the snapshot to compute a destination point, and it moves toward…

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…

We consider an old question of Slaman and Steel: whether Turing equivalence is an increasing union of Borel equivalence relations none of which contain a uniformly computable infinite sequence. We show this question is deeply connected to…

It is known that no quantum process can produce a predetermined superposition of unknown arbitrary states. It has already been shown that with some partial information about the states, one can produce with some probability such…