Related papers: Ordinal computers
In this paper, we investigate the problem of synthesizing computable functions of infinite words over an infinite alphabet (data $\omega$-words). The notion of computability is defined through Turing machines with infinite inputs which can…
Quantum computing promises transformational gains for solving some problems, but little to none for others. For anyone hoping to use quantum computers now or in the future, it is important to know which problems will benefit. In this paper,…
There exists a huge number of numerical methods that iteratively construct approximations to the solution $y(x)$ of an ordinary differential equation (ODE) $y'(x)=f(x,y)$ starting from an initial value $y_0=y(x_0)$ and using a finite…
Quantum computing promises the ability to compute properties of quantum systems exponentially faster than classical computers. Quantum advantage is achieved when a practical problem is solved more efficiently on a quantum computer than on a…
Online algorithm is a well-known computational model. We introduce quantum online algorithms and investigate them with respect to a competitive ratio in two points of view: space complexity and advice complexity. We start with exploring a…
A typical oracle problem is finding which software program is installed on a computer, by running the computer and testing its input-output behaviour. The program is randomly chosen from a set of programs known to the problem solver. As…
Systems are growing into more complex ones for developing and maintaining. Existing systems which do not have much in common on the first look are connected, due to the technical progress, even if it was never intended that way. It is an…
Quantum computing has the potential to solve many computational problems exponentially faster than classical computers. The high shares of renewables and the wide deployment of converter-interfaced resources require new tools that shall…
Fuelled by increasing computer power and algorithmic advances, machine learning techniques have become powerful tools for finding patterns in data. Since quantum systems produce counter-intuitive patterns believed not to be efficiently…
The Turing machine is one of the simple abstract computational devices that can be used to investigate the limits of computability. In this paper, they are considered from several points of view that emphasize the importance and the…
We consider a first-order logic for the integers with addition. This logic extends classical first-order logic by modulo-counting, threshold-counting and exact-counting quantifiers, all applied to tuples of variables (here, residues are…
Recently developed quantum algorithms suggest that quantum computers can solve certain problems and perform certain tasks more efficiently than conventional computers. Among other reasons, this is due to the possibility of creating…
A computer which has access to a closed timelike curve, and can thereby send the results of calculations into its own past, can exploit this to solve difficult computational problems efficiently. I give a specific demonstration of this for…
We show that the protocol recently proposed by Hosten et al. does not allow all possible results of a computation to be obtained counterfactually, as was claimed. It only gives a counterfactual outcome for one of the computer outputs.…
Infinite time Turing machines (ITTMs) have been introduced by Hamkins and Lewis in their seminal article arXiv:math/9808093. The strength of the model comes from a limit rule which allows the ITTM to compute through ordinal stages. This…
The field of quantum algorithms aims to find ways to speed up the solution of computational problems by using a quantum computer. A key milestone in this field will be when a universal quantum computer performs a computational task that is…
Today's PCs can directly manipulate numbers not longer than 64 bits because the size of the CPU registers and the data-path are limited. Consequently, arithmetic operations such as addition, can only be performed on numbers of that length.…
In recent years, a number of prominent computer scientists, along with academics in fields such as philosophy and physics, have lent credence to the notion that machines may one day become as large as humans. Many have further argued that…
We determine the complexity of counting models of bounded size of specifications expressed in Linear-time Temporal Logic. Counting word models is #P-complete, if the bound is given in unary, and as hard as counting accepting runs of…
Cantor's ordinal numbers, a powerful extension of the natural numbers, are a cornerstone of set theory. They can be used to reason about the termination of processes, prove the consistency of logical systems, and justify some of the core…