Related papers: Towards a Self-Replicating Turing Machine
For quantum Turing machines we present three elements: Its components, its time evolution operator and its local transition function. The components are related with the components of deterministic Turing machines, the time evolution…
Various specifiable combinatorial structures, with d extensive parameters, can be exactly sampled both by the recursive method, with linear arithmetic complexity if a heavy preprocessing is performed, or by the Boltzmann method, with…
We describe the Turing Machine, list some of its many influences on the theory of computation and complexity of computations, and illustrate its importance.
We introduce two notions of effective reducibility for set-theoretical statements, based on computability with Ordinal Turing Machines (OTMs), one of which resembles Turing reducibility while the other is modelled after Weihrauch…
Validation of a presumably universal theory, such as quantum mechanics, requires a quantum mechanical description of systems that carry out theoretical calculations and experiments. The description of quantum computers is under active…
We define a generalization of the Turing machine that computes on general sets. Our main theorem states that the class of generalized Turing machine computable functions and the class of Set Recursive functions coincide.
This paper introduces abstractions that are meaningful for computers and that can be built and used according to computers' own criteria, i.e., computable abstractions. It is analyzed how abstractions can be seen to serve as the building…
Informally, an extractor delivers perfect randomness from a source that may be far away from the uniform distribution, yet contains some randomness. This task is a crucial ingredient of any attempt to produce perfectly random…
Inspired by the emergent membrane computing (P Systems) concepts, some efforts are carried out introducing simulation models, some are software oriented, and others are hardware, yet all are applied with the current vision of the…
This paper presents our approach to use refactoring techniques together with code generation. Refactoring is particularly useful if not only the generated classes but also the generator itself can be adapted in an automatic fashion. We have…
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…
we envisage a novel quantum cloning machine, which takes an input state and produces an output state whose success branch can exist in a linear superposition of multiple copies of the input state and the failure branch exist in a…
Most modern classical processors support so-called von Neumann architecture with program and data registers. In present work is revisited similar approach to models of quantum processors. Deterministic programmable quantum gate arrays are…
This short survey of recent work in tile self-assembly discusses the use of simulation to classify and separate the computational and expressive power of self-assembly models. The journey begins with the result that there is a single…
We introduce a parallelizable simplification of Neural Turing Machine (NTM), referred to as P-NTM, which redesigns the core operations of the original architecture to enable efficient scan-based parallel execution. We evaluate the proposed…
This article aims at providing signal machines as small as possible able to perform any computation (in the classical understanding). After presenting signal machines, it is shown how to get universal ones from Turing machines,…
We give small universal Turing machines with state-symbol pairs of (6, 2), (3, 3) and (2, 4). These machines are weakly universal, which means that they have an infinitely repeated word to the left of their input and another to the right.…
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…
If we define classical foundational concepts constructively, and introduce non-algorithmic effective methods into classical mathematics, then we can bridge the chasm between truth and provability, and define computational methods that are…
The cloning of quantum variables with continuous spectra is analyzed. A universal - or Gaussian - quantum cloning machine is exhibited that copies equally well the states of two conjugate variables such as position and momentum. It also…