Related papers: Zeno machines and Running Turing machine for infin…
Quantum simulation of lattice gauge theories is a promising tool for the study of many complicated problems including ones with real-time dynamics. For gauge theories, however, there is a major challenge in maintaining gauge invariance…
We introduce semaphore codes associated to a Turing machine via resets. Semaphore codes provide an approximation theory for resets. In this paper we generalize the set-up of our previous paper "Random walks on semaphore codes and delay de…
The behavior displayed by a quantum system when it is perturbed by a series of von Neumann measurements along time is analyzed. Because of the similarity between this general process with giving a deck of playing cards a shuffle, here it is…
For each Turing machine T, we construct an algebra A'(T) such that the variety generated by A'(T) has definable principal subcongruences if and only if T halts, thus proving that the property of having definable principal subcongruences is…
The interplay between quantum-mechanical properties, such as coherence, and classical notions, such as energy, is a subtle topic at the forefront of quantum thermodynamics. The traditional Carnot argument limits the conversion of heat to…
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…
There are both practical and foundational motivations to consider the thermodynamics of quantum systems at small scales. Here we address the issue of autonomous quantum thermal machines that are tailored to achieve some specific…
The article contains an outline of a possible new direction for Computability Logic (see www.csc.villanova.edu/~japaridz/CL/ ), focused on computability without infinite memory or other impossible-to-possess computational resources. The new…
Among the fundamental questions in computer science, at least two have a deep impact on mathematics. What can computation compute? How many steps does a computation require to solve an instance of the 3-SAT problem? Our work addresses the…
We prove that any Turing machine running on inputs of arbitrary length can be simulated by a constant bit-size transformer, as long as the context window is sufficiently long. This improves previous works, which require scaling up either…
Based on the propositional description of even Goldbach conjecture, in order to verify the truth of even Goldbach conjecture, we will deeply discuss this question and present a new computing model of $G{{N}_{e}}TM$ Turing Machine. This…
By closely rereading the original Turing's 1936 article, we can gain insight about that it is based on the claim to have defined a number which is not computable, arguing that there can be no machine computing the diagonal on the…
We derive the statistics of the efficiency under the assumption that thermodynamic fluxes fluctuate with normal law, parametrizing it in terms of time, macroscopic efficiency, and a coupling parameter $\zeta$. It has a peculiar behavior: No…
Near term quantum hardware promises to achieve quantum supremacy. From a quantum dynamical point of view, however, it is not unambiguously clear whether fundamental peculiarities of quantum physics permit any arbitrary speed-ups in real…
Many programs allow the user to input data several times during its execution. If the program runs forever the user may input data infinitely often. A program terminates if it terminates no matter what the user does. We discuss various ways…
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…
The quantum Zeno effect consists in the hindrance of the evolution of a quantum system that is very frequently monitored and found to be in its initial state at every single measurement. On the basis of the correct formula for the survival…
This dissertation investigates questions arising in the consistent histories formulation of the quantum mechanics of closed systems. Various criteria for approximate consistency are analysed. The connection between the Dowker-Halliwell…
In a reachability-time game, players Min and Max choose moves so that the time to reach a final state in a timed automaton is minimised or maximised, respectively. Asarin and Maler showed decidability of reachability-time games on strongly…
One of the major objectives of Artificial Intelligence is to design learning algorithms that are executed on a general purposes computational machines such as human brain. Neural Turing Machine (NTM) is a step towards realizing such a…