Related papers: Computational Dynamical Systems
The presence of symmetries, be they discrete or continuous, in a physical system typically leads to a reduction in the problem to be solved. Here we report that neither translational invariance nor rotational invariance reduce the…
As in the car industry for quite some time, dynamic simulation of complete vehicles is being practiced more and more in the development of off-road machinery. However, specific questions arise due not only to company structure and size, but…
A properly designed controller can help improve the quality of experimental measurements or force a dynamical system to follow a completely new time-evolution path. Recent developments in deep reinforcement learning have made steep advances…
In this paper we review recent work on novel computing paradigms using coupled oscillatory dynamical systems. We explore systems of relaxation oscillators based on linear state transitioning devices, which switch between two discrete states…
Building software-driven systems that are easily understood becomes a challenge, with their ever-increasing complexity and autonomy. Accordingly, recent research efforts strive to aid in designing explainable systems. Nevertheless, a common…
Robustness of a distributed computing system is defined as the ability to maintain its performance in the presence of uncertain parameters. Uncertainty is a key problem in heterogeneous (and even homogeneous) distributed computing systems…
According to the Church-Turing Thesis (CTT), effective formal behaviours can be simulated by Turing machines; this has naturally led to speculation that physical systems can also be simulated computationally. But is this wider claim true,…
Symbolic models are abstract descriptions of continuous systems in which symbols represent aggregates of continuous states. In the last few years there has been a growing interest in the use of symbolic models as a tool for mitigating…
We discuss classical and quantum computations in terms of corresponding Hamiltonian dynamics. This allows us to introduce quantum computations which involve parallel processing of both: the data and programme instructions. Using mixed…
Computers are deterministic dynamical systems (CHAOS 19:033124, 2009). Among other things, that implies that one should be able to use deterministic forecast rules to predict their behavior. That statement is sometimes-but not always-true.…
The intuition that a long history is required for the emergence of complexity in natural systems is formalized using the notion of depth. The depth of a system is defined in terms of the number of parallel computational steps needed to…
In a recent preprint [1] (arXiv:2503.05693), Tindall et al. presented impressive classical simulations of quantum dynamics using tensor networks. Their methods represent a significant improvement in the classical state of the art, and in…
Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by being based on two…
We study deterministic and quantum dynamics from a constructive "finite" point of view, since the introduction of a continuum, or other actual infinities in physics poses serious conceptual and technical difficulties, without any need for…
Recently Quantum Computation has generated a lot of interest due to the discovery of a quantum algorithm which can factor large numbers in polynomial time. The usefulness of a quantum com puter is limited by the effect of errors. Simulation…
A key concern in modern distributed systems is to avoid the cost of coordination while maintaining consistent semantics. Until recently, there was no answer to the question of when coordination is actually required. In this paper we present…
This is the first of a series of papers in which we study deep computations (ultracomputations) and deep iterates, formalizing the ideas of "asymptotic limit" of computations and compositional iterates, respectively. In this first paper of…
This paper is motivated by the theory of sequential dynamical systems, developed as a basis for a mathematical theory of computer simulation. It contains a classification of finite dynamical systems on binary strings, which are obtained by…
Through a straightforward Bayesian approach we show that under some general conditions a maximum running time, namely the number of discrete steps performed by a computer program during its execution, can be defined such that the…
We study the paradoxical aspects of closed time-like curves and their impact on the theory of computation. After introducing the $\text{TM}_\text{CTC}$, a classical Turing machine benefiting CTCs for backward time travel, Aaronson et al.…