Related papers: What can we learn from universal Turing machines?
We explore the relationship between Turing completeness and topological entropy of dynamical systems. We first prove that a natural class of Turing machines that we call "branching Turing machines" (which includes most of the known examples…
The abstract notion of a Universal Turing machine cannot exist as a physical subsystem without the introduction of noise from an external energy source. Like all other physical systems, physical Turing machines must convert energy sourced…
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…
We advance a Bayesian concept of 'intrinsic asymptotic universality' taking to its final conclusions previous conceptual and numerical work based upon a concept of a reprogrammability test and an investigation of the complex qualitative…
The traditional process of building interactive machine learning systems can be viewed as a teacher-learner interaction scenario where the machine-learners are trained by one or more human-teachers. In this work, we explore the idea of…
Characterising the intelligence of biological organisms is challenging. This work considers intelligent algorithms developed evolutionarily within neural systems. Mathematical analyses unveil a natural equivalence between canonical neural…
We propose reactive Turing machines (RTMs), extending classical Turing machines with a process-theoretical notion of interaction, and use it to define a notion of executable transition system. We show that every computable transition system…
This paper presents the implementation of a self-replicating finite-state machine (FSM) and a self-replicating Turing Machine (TM) using bio-inspired mechanisms. Building on previous work that introduced self-replicating structures capable…
Quantum technology has the potential to revolutionize how we acquire and process experimental data to learn about the physical world. An experimental setup that transduces data from a physical system to a stable quantum memory, and…
The human brain has many remarkable information processing characteristics that deeply puzzle scientists and engineers. Among the most important and the most intriguing of these characteristics are the brain's broad universality as a…
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…
We outline the construction of a molecular system that could, in principle, implement a thermodynamically reversible Universal Turing Machine (UTM). By proposing a concrete-albeit idealised-design and operational protocol, we reveal…
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 paper presents an algebraic theory of instruction sequences with instructions for Turing tapes as basic instructions, the behaviours produced by the instruction sequences concerned under execution, and the interaction between such…
We describe how one may go about performing quantum computation with arbitrary "quantum stuff", as long as it has some basic physical properties. Imagine a long strip of stuff, equipped with regularly spaced wires to provide input settings…
Contrary to the classical case, the relation between quantum programming languages and quantum Turing Machines (QTM) has not being fully investigated. In particular, there are features of QTMs that have not been exploited, a notable example…
We discuss various universality aspects of numerical computations using standard algorithms. These aspects include empirical observations and rigorous results. We also make various speculations about computation in a broader sense.
The rapid evolution of intelligent electronic devices makes information technology, computer science and electronics strongly related to the teaching of natural sciences. Today almost everybody has a smart phone that can convert light,…
Universal Turing Machines [29, 10, 18] are well known in computer science but they are about manual programming for general purposes. Although human children perform conscious learning (i.e., learning while being conscious) from infancy…
Given the importance of integrating of explainability into machine learning, at present, there are a lack of pedagogical resources exploring this. Specifically, we have found a need for resources in explaining how one can teach the…