Related papers: Infinite Time Turing Machines: Supertask Computati…
Infinite time Turing machines extend the classical Turing machine concept to transfinite ordinal time, thereby providing a natural model of infinitary computability that sheds light on the power and limitations of supertask algorithms.
We extend in a natural way the operation of Turing machines to infinite ordinal time, and investigate the resulting supertask theory of computability and decidability on the reals. The resulting computability theory leads to a notion of…
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.
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…
We describe the basic theory of infinite time Turing machines and some recent developments, including the infinite time degree theory, infinite time complexity theory, and infinite time computable model theory. We focus particularly on the…
We introduce a model of infinitary computation which enhances the infinite time Turing machine model slightly but in a natural way by giving the machines the capability of detecting cardinal stages of computation. The computational strength…
Infinite time Turing machines with only one tape are in many respects fully as powerful as their multi-tape cousins. In particular, the two models of machine give rise to the same class of decidable sets, the same degree structure and, at…
We define a new transfinite time model of computation, infinite time cellular automata. The model is shown to be as powerful than infinite time Turing machines, both on finite and infinite inputs; thus inheriting many of its properties. We…
This work establishes a rigorous theoretical foundation for analyzing deep learning systems by leveraging Infinite Time Turing Machines (ITTMs), which extend classical computation into transfinite ordinal steps. Using ITTMs, we reinterpret…
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…
This paper analyzes infinitary nondeterministic computability theory. The main result is D $\ne$ ND $\cap$ coND where D is the class of sets decidable by infinite time Turing machines and ND is the class of sets recognizable by a…
We describe various computational models based initially, but not exclusively, on that of the Turing machine, that are generalized to allow for transfinitely many computational steps. Variants of such machines are considered that have…
We propose a notion of autoreducibility for infinite time computability and explore it and its connection with a notion of randomness for infinite time machines.
Using nonstandard analysis, we will extend the classical Turing machines into the internal Turing machines. The internal Turing machines have the capability to work with infinite ($*$-finite) number of bits while keeping the finite…
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 the question whether there is an infinitary analogue of the Church-Turing-thesis. To this end, we argue that there is an intuitive notion of transfinite computability and build a canonical model, called Idealized Agent Machines…
This note introduces a generalization to the setting of infinite-time computation of the busy beaver problem from classical computability theory, and proves some results concerning the growth rate of an associated function. In our view,…
We introduce an analog of the theory of Borel equivalence relations in which we study equivalence relations that are decidable by an infinite time Turing machine. The Borel reductions are replaced by the more general class of infinite time…
Finite Turing computation has a fundamental symmetry between inputs, outputs, programs, time, and storage space. Standard models of transfinite computational break this symmetry; we consider ways to recover it and study the resulting model…
This paper discusses "computational" systems capable of "computing" functions not computable by predefined Turing machines if the systems are not isolated from their environment. Roughly speaking, these systems can change their finite…