Related papers: Infinite Time Recognizability from Random Oracles …
Infinite Time Register Machines ($ITRM$'s) are a well-established machine model for infinitary computations. Their computational strength relative to oracles is understood, see e.g. Koepke (2009), Koepke and Welch (2011) and Koepke and…
A concept of randomness for infinite time register machines (ITRMs) is defined and studied. In particular, we show that for this notion of randomness, computability from mutually random reals implies computability and that an analogue of…
A concept of randomness for infinite time register machines (ITRMs), resembling Martin-L\"of-randomness, is defined and studied. In particular, we show that for this notion of randomness, computability from mutually random reals implies…
Exploring further the properties of ITRM-recognizable reals, we provide a detailed analysis of recognizable reals and their distribution in G\"odels constructible universe L. In particular, we show that, for unresetting infinite time…
We study randomness beyond $\Pi^1_1$-randomness and its Martin-L\"of type variant, introduced in \cite{MR2340241} and further studied in \cite{Continuous-higher-randomness}. The class given by the infinite time Turing machines (\ITTM s),…
We consider the following problem for various infinite time machines. If a real is computable relative to large set of oracles such as a set of full measure or just of positive measure, a comeager set, or a nonmeager Borel set, is it…
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.
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…
We consider recognizability for Infinite Time Blum-Shub-Smale machines, a model of infinitary computability introduced in Koepke and Seyfferth [KS]. In particular, we show that the lost melody theorem (originally proved for ITTMs in Hamkins…
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 two notions of effective reducibility for set-theoretical statements, based on computability with Ordinal Turing Machines (OTMs), one of which resembles Turing reducibility while the other is modelled after Weihrauch…
Recently we have introduced a new model of infinite computation by extending the operation of ordinary Turing machines into transfinite ordinal time. In this paper we will show that the infinite time Turing machine analogue of Post's…
For exponentially closed ordinals $\alpha$, we consider recognizability of constructible subsets of $\alpha$ for $\alpha$-(w)ITRMs and their distribution in the constructible hierarchy. In particular, for $\alpha$-ITRMs, we show that, there…
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…
We find a countable partition $P$ on\textbf{} a Lebesgue space, labeled $\{1,2,3...$\}, for any non-periodic measure preserving transformation $T$ such that $P$ generates $T$ and for the $T,P$ process, if you see an $n$ on time -1 then you…
Nonequilibrium equalities have attracted considerable interest in the context of statistical mechanics and information thermodynamics. What is remarkable about nonequilibrium equalities is that they apply to rather general nonequilibrium…
Reversible computing can reduce the energy dissipation of computation, which can improve cost-efficiency in some contexts. But the practical applicability of this method depends sensitively on the space and time overhead required by…
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…
This article expands our work in [Ca16]. By its reliance on Turing computability, the classical theory of effectivity, along with effective reducibility and Weihrauch reducibility, is only applicable to objects that are either countable or…
Turing's famous 'machine' framework provides an intuitively clear conception of 'computing with real numbers'. A recursive counterexample to a theorem shows that the theorem does not hold when restricted to computable objects. These…