Related papers: Universal Computation Is 'Almost Surely' Chaotic
Autonomous randomly coupled neural networks display a transition to chaos at a critical coupling strength. We here investigate the effect of a time-varying input on the onset of chaos and the resulting consequences for information…
Chaotic functions are characterized by sensitivity to initial conditions, transitivity, and regularity. Providing new functions with such properties is a real challenge. This work shows that one can associate with any Boolean network a…
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.…
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…
Generic computability has been studied in group theory and we now study it in the context of classical computability theory. A set A of natural numbers is generically computable if there is a partial computable function f whose domain has…
This paper presents an analysis of the concept of capacity for noisy computations, i.e. algorithms implemented by unreliable computing devices (e.g. noisy Turing Machines). The capacity of a noisy computation is defined and justified by…
The dynamics of the tubular chemical reactor with mass recycle were examined. In such a system, temperature and concentrations may oscillate chaotically. This means that state variable values are then unpredictable. In this paper it has…
The dynamics of one dimensional iterative maps in the regime of fully developed chaos is studied in detail. Motivated by the observation of dynamical structures around the unstable fixed point we introduce the geometrical concept of a…
Deterministic chaos permits a precise notion of a "perfect measurement" as one that, when obtained repeatedly, captures all of the information created by the system's evolution with minimal redundancy. Finding an optimal measurement is…
Infinite time Turing machines are extended in several ways to allow for iterated oracle calls. The expressive power of these machines is discussed and in some cases determined.
The effect of noise on self-similar set is studied. The iteratie procedure used to generate the self-similar set is moidified by adding a stochastic variable to the diameter of generating sets at each iteration. The noise may causes the…
In this paper we present a general result with an easily checkable condition that ensures a transition from chaotic regime to regular regime in random dynamical systems with additive noise. We show how this result applies to a prototypical…
It has been demonstrated that cellular automata had the highest computational capacity at the edge of chaos, the parameter at which their behavior transitioned from ordered to chaotic. This same concept has been applied to reservoir…
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…
A remarkable new definition of a self-delimiting universal Turing machine is presented that is easy to program and runs very quickly. This provides a new foundation for algorithmic information theory. This new universal Turing machine is…
Fundamental problems of periodicity and transient process to periodicity of chaotic trajectories in computer realization with finite computation precision is investigated by taking single and coupled Logistic maps as examples. Empirical…
According to Deutsch, a universal quantum Turing machine (UQTM) is able to perform, in repeating a fixed unitary transformation on the total system, an arbitrary unitary transformation on an arbitrary data state, by including a program as…
Machine learning processes, e.g. ''learning in games'', can be viewed as non-linear dynamical systems. In general, such systems exhibit a wide spectrum of behaviors, ranging from stability/recurrence to the undesirable phenomena of chaos…
The complexity of cellular automata is traditionally measured by their computational capacity. However, it is difficult to choose a challenging set of computational tasks suitable for the parallel nature of such systems. We study the…
We describe adaptive control algorithms whereby a chaotic dynamical system can be steered to a target state with desired characteristics. A specific implementation considered has the objective of directing the system to a state which is…