Related papers: The Church-Turing thesis as a guiding principle fo…
A critical analysis of the feasibility of reversible computing is performed. The key question is: Is it possible to build a completely reversible computer? A closer look into the internal aspects of the reversible computing as well as the…
We introduce infinite time computable model theory, the computable model theory arising with infinite time Turing machines, which provide infinitary notions of computability for structures built on the reals R. Much of the finite time…
Before Alan Turing made his crucial contributions to the theory of computation, he studied the question of whether quantum mechanics could throw light on the nature of free will. This article investigates the roles of quantum mechanics and…
It is considered an interdependence of the theory of quantum computing and some perspective information technologies. A couple of illustrative and useful examples are discussed. The reversible computing from very beginning had the serious…
In the present work, a new time-dependent exchange theory is presented wherein the symmetry constraints, on a multi-electron wavefunction, are properly accounted for. In so doing, the equations of motion, incorporating the required…
The Independence Postulate (IP) is a finitary Church-Turing Thesis, saying mathematical sequences are independent from physical ones. Modelling observations as infinite sequences of real numbers, IP implies the existence of anomalies.
The notion from ab-initio molecular dynamics simulations that nuclear motion is best described by classical Newton dynamics instead of the time-dependent Schr{\"o}dinger equation is substantiated. In principle a single experiment should…
Consider the scenario, in which human civilization undergoes periodic eras of progression and regression, and consequently, changes in cosmological knowledge are cyclic. There exist solutions of general theory of relativity, such as the…
An "anorthodox" explanation of the recently discovered (1998) "acceleration" of the Universe is proposed.
The overarching theme of the following pages is that mathematical logic -- centered around the incompleteness theorems -- is first and foremost an investigation of $\textit{computation}$, not arithmetic. Guided by this intuition we will…
Recent theoretical results confirm that quantum theory provides the possibility of new ways of performing efficient calculations. The most striking example is the factoring problem. It has recently been shown that computers that exploit…
The uncertainty principle is a cornerstone of modern physics, and its implications have a fundamental impact on theoretical and applied quantum mechanics. The aim of this thesis is to study and apply the uncertainty relations between time…
Cirquent calculus is a proof system manipulating circuit-style constructs rather than formulas. Using it, this article constructs a sound and complete axiomatization CL16 of the propositional fragment of computability logic (the…
This paper provides a new and more direct proof of the assertion that a Turing computable function of the natural numbers is primitive recursive if and only if the time complexity of the corresponding Turing machine is bounded by a…
The emphasis is made on the juxtaposition of (quantum~theorem) proving versus quantum (theorem~proving). The logical contents of verification of the statements concerning quantum systems is outlined. The Zittereingang (trembling input)…
Tethered particle motion experiments are versatile single-molecule techniques enabling one to address in vitro the molecular properties of DNA and its interactions with various partners involved in genetic regulations. These techniques…
The upper limit on what is computable in our universe is unknown, but widely believed to be set by the Turing machine -- with a function being physically computable if and only if it is Turing-computable. I show how this apparently mild…
We give a condensed and accessible summary of a recent derivation of quantum theory from information-theoretic principles, and use it to study the consequences of this and other reconstructions for our conceptual understanding of the…
Are minds subject to laws of physics? Are the laws of physics computable? Are conscious thought processes computable? Currently there is little agreement as to what are the right answers to these questions. Penrose goes one step further and…
Kaluza's mertic with the cylinder condition is considered without the weak gravitational field approximation. It is shown that these hypoteses lead to a non-gauge-invariant electromagnetic theory in a curved space-time. The problem of…