相关论文: Strong Determinism vs. Computability

In the first of this pair of papers, it was proven that that no physical computer can correctly carry out all computational tasks that can be posed to it. The generality of this result follows from its use of a novel definition of…

Computational problems are classified into computable and uncomputable problems. If there exists an effective procedure (algorithm) to compute a problem then the problem is computable otherwise it is uncomputable. Turing machines can…

Recent work has examined how undecidable problems can arise in quantum information science. We augment this by introducing three new undecidable problems stated in terms of tensor networks. These relate to ideas of Penrose about the…

It is argued that any possible definition of a realistic physics theory -- i.e., a mathematical model representing the real world -- cannot be considered comprehensive unless it is supplemented with requirement of being computationally…

Computers are physical systems: what they can and cannot do is dictated by the laws of physics. In particular, the speed with which a physical device can process information is limited by its energy and the amount of information that it can…

We clarify the confusion, misunderstanding and misconception that the physical finiteness of the universe, if the universe is indeed finite, would rule out all hypercomputation, the kind of computation that exceeds the Turing computability,…

Theories for reasoning about programs with effects initially focused on basic manipulation of lists and other mutable data. The next challenge was to consider higher-order programming, adding functions as first class objects to mutable…

We look at consciousness through the lens of Theoretical Computer Science, a branch of mathematics that studies computation under resource limitations, distinguishing functions that are efficiently computable from those that are not. From…

The study of intelligent systems explains behaviour in terms of economic rationality. This results in an optimization principle involving a function or utility, which states that the system will evolve until the configuration of maximum…

We develop a complexity theory for approximate real computations. We first produce a theory for exact computations but with condition numbers. The input size depends on a condition number, which is not assumed known by the machine. The…

General relativity treats spacetime as dynamical and exhibits its breakdown at singularities. This failure is interpreted as evidence that quantum gravity is not a theory formulated within spacetime; instead, it must explain the very…

Hypercomputation is a relatively new branch of computer science that emerged from the idea that the Church--Turing Thesis, which is supposed to describe what is computable and what is noncomputable, cannot possible be true. Because of its…

The problem of defining and locating free will (FW) in physics is studied. On basis of logical paradoxes, we argue that FW has a meta-theoretic character, like the concept of truth in Tarski's undefinability theorem. Free will exists…

Most physics theories are deterministic, with the notable exception of quantum mechanics which, however, comes plagued by the so-called measurement problem. This state of affairs might well be due to the inability of standard mathematics to…

I am most honoured to have the privilege to present the Foreword to this fascinating and wonderfully varied collection of contributions, concerning the nature of computation and of its deep connection with the operation of those basic laws,…

Physical modeling closes the gap between perception in terms of measurements and abstraction in terms of theoretical models. Physical modeling is a major objective in physics and is generally regarded as a creative process. How good are…

Recent theoretical results confirm that quantum theory provides the possibility of new ways of performing efficient calculations. The most striking example is the factoring problem. It has recently been shown that computers that exploit…

Computational Intelligence is a dead-end attempt to recreate human-like intelligence in a computing machine. The goal is unattainable because the means chosen for its accomplishment are mutually inconsistent and contradictory:…

Trying to be effective (no matter who exactly and in what field) a person face the problem which inevitably destroys all our attempts to easily get to a desired goal. The problem is the existence of some insuperable barriers for our mind,…

Before Alan Turing made his crucial contributions to the theory of computation, he studied the question of whether quantum mechanics could throw light on the nature of free will. This article investigates the roles of quantum mechanics and…