Related papers: Towards a Self-Replicating Turing Machine

It has been argued that a central objective of nanotechnology is to make products inexpensively, and that self-replication is an effective approach to very low-cost manufacturing. The research presented here is intended to be a step towards…

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…

In the abstract Tile Assembly Model, self-assembling systems consisting of tiles of different colors can form structures on which colored patterns are ``painted.'' We explore the complexity, in terms of the numbers of unique tile types…

We describe a method to axiomatize computations in deterministic Turing machines. When applied to computations in non-deterministic Turing machines, this method may produce contradictory (and therefore trivial) theories, considering…

We have generalised the properties with the tensor product, of one 4x4 matrix which is a permutation matrix, and we call a tensor commutation matrix. Tensor commutation matrices can be constructed with or without calculus. A formula allows…

A Riemannian or pseudo-Riemannian (or conformal) structure is conformally Einstein if and only if there is a suitably generic parallel section of a certain vector bundle -- the so-called standard conformal tractor bundle. We show that this…

In this paper we present a model containing modifications to the Signal-passing Tile Assembly Model (STAM), a tile-based self-assembly model whose tiles are capable of activating and deactivating glues based on the binding of other glues.…

Using tools from topology and functional analysis, we provide a framework where artificial neural networks, and their architectures, can be formally described. We define the notion of machine in a general topological context and show how…

The von Neumann architecture for a classical computer comprises a central processing unit and a memory holding instructions and data. We demonstrate a quantum central processing unit that exchanges data with a quantum random-access memory…

A generalization of the semisimplicity concept for polyadic algebraic structures is proposed. If semisimple structures can be presented in block diagonal matrix form (resulting in the Wedderburn decomposition), a general form of polyadic…

This paper presents a theoretical, idealized model of the thinking process with the following characteristics: 1) the model can produce complex thought sequences and can be generalized to new inputs, 2) it can receive and maintain input…

There are enormous amount of examples of Computation in nature, exemplified across multiple species in biology. One crucial aim for these computations across all life forms their ability to learn and thereby increase the chance of their…

This talk advocates intrinsic universality as a notion to identify simple cellular automata with complex computational behavior. After an historical introduction and proper definitions of intrinsic universality, which is discussed with…

We introduce and analyze a model for self-reconfigurable robots made up of unit-cube modules. Compared to past models, our model aims to newly capture two important practical aspects of real-world robots. First, modules often do not occupy…

Turing Machines are universal computing machines in theory. It has been a long debate whether Turing Machines can simulate the consciousness mind behaviors in the materialistic universe. Three different hypotheses come out of such debate,…

The decomposition of large unitary matrices into smaller ones is important, because it provides ways to realization of classical and quantum information processing schemes. Today, most of the methods use planar meshes of tunable two-channel…

We describe the basic theory of infinite time Turing machines and some recent developments, including the infinite time degree theory, infinite time complexity theory, and infinite time computable model theory. We focus particularly on the…

Nanomechanical computers promise a greatly improved energetic efficiency compared to their electrical counterparts. However, progress towards this goal is hindered by a lack of modular components, such as logic gates or transistors, and…

Computational problems are classified into computable and uncomputable problems. If there exists an effective procedure (algorithm) to compute a problem then the problem is computable otherwise it is uncomputable. Turing machines can…

We introduce an algorithm that conjectures the structure of a permutation class in the form of a disjoint cover of "rules"; similar to generalized grid classes. The cover is usually easily verified by a human and translated into an…