相关论文: Finiteness of the universe and computation beyond …

This article reviews the history of digital computation, and investigates just how far the concept of computation can be taken. In particular, I address the question of whether the universe itself is in fact a giant computer, and if so,…

Recent work by Faizal et al. (2025) claims that G\"odelian undecidability of non-algorithmic truths in our universe imply the impossibility of a formal, algorithmic simulation of the universe. This paper clarifies the distinction between…

Notoriously, quantum computation shatters complexity theory, but is innocuous to computability theory. Yet several works have shown how quantum theory as it stands could breach the physical Church-Turing thesis. We draw a clear line as to…

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.

This short paper proposes an alternative theory to Anthropic Principle. According to our interpretation, the Universe is not "fine-tuned" for life, but "roughly-tuned" for computation and its biofilness is only a phenomenon. This standpoint…

The upper limit on what is computable in our universe is unknown, but widely believed to be set by the Turing machine -- with a function being physically computable if and only if it is Turing-computable. I show how this apparently mild…

Recent works have independently suggested that Quantum Mechanics might permit for procedures that transcend the power of Turing Machines as well as of `standard' Quantum Computers. These approaches rely on and indicate that Quantum…

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…

The nature of quantum computation is discussed. It is argued that, in terms of the amount of information manipulated in a given time, quantum and classical computation are equally efficient. Quantum superposition does not permit quantum…

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…

Turing machines and spin models share a notion of universality according to which some simulate all others. Is there a theory of universality that captures this notion? We set up a categorical framework for universality which includes as…

We argue that whether the universe is infinite or finite is less crucial than usually supposed. Paradoxes of repeating behaviour in the infinite, or eternal inflationary, universe can be alleviated by a realistic definition of differing…

We discuss some claims that certain UCOMP devices can perform hypercomputation (compute Turing-uncomputable functions) or perform super-Turing computation (solve NP-complete problems in polynomial time). We discover that all these claims…

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…

Although various limits on the predicability of physical phenomena as well as on physical knowables are commonly established and accepted, we challenge their ultimate validity. More precisely, we claim that fundamental limits arise only…

Beginning with Turing's seminal work in 1950, artificial intelligence proposes that consciousness can be simulated by a Turing machine. This implies a potential theory of everything where the universe is a simulation on a computer, which…

If we define classical foundational concepts constructively, and introduce non-algorithmic effective methods into classical mathematics, then we can bridge the chasm between truth and provability, and define computational methods that are…

We use fast-growing finite and infinite sequences of natural numbers and more complicated constructs to define models of hypercomputation and interpret non-arithmetic predicates, with the strongest extensions reaching full second order…

When we want to predict the future, we compute it from what we know about the present. Specifically, we take a mathematical representation of observed reality, plug it into some dynamical equations, and then map the time-evolved result back…

The ultimate limits of computation are not just logical, but physical. We investigate the physical resources -- time, energy, entropy, and free energy -- required to perform computational work. We apply the resulting measures of physical…