Related papers: Cosmic Logic: a Computational Model
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…
Computational Logic is the use of computers to establish facts in a logical formalism. Originating in 19th-century attempts to understand the nature of mathematical reasoning, the subject now comprises a wide variety of formalisms,…
Although the Turing-machine model of computation is widely used in computer science it is fundamentally inadequate as a foundation for the theory of modern scientific computation. The real-number model is described as an alternative.…
We have defined the Conscious Turing Machine (CTM) for the purpose of investigating a Theoretical Computer Science (TCS) approach to consciousness. For this, we have hewn to the TCS demand for simplicity and understandability. The CTM is…
Even when completely and consistently formulated, a fundamental theory of physics and cosmological boundary conditions may not give unambiguous and unique predictions for the universe we observe; indeed inflation, string/M theory, and…
We develop synthetic notions of oracle computability and Turing reducibility in the Calculus of Inductive Constructions (CIC), the constructive type theory underlying the Coq proof assistant. As usual in synthetic approaches, we employ a…
Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by having it follow from…
We investigate a variant of the fuel-based approach to modeling diverging computation in type theories and use it to abstractly capture the essence of oracle Turing machines. The resulting objects we call continuous machines. We prove that…
It is possible in principle to construct quantum mechanical observables and unitary operators which, if implemented in physical systems as measurements and dynamical evolution, would contradict the Church-Turing thesis, which lies at the…
Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…
We give new evidence that quantum computers -- moreover, rudimentary quantum computers built entirely out of linear-optical elements -- cannot be efficiently simulated by classical computers. In particular, we define a model of computation…
We propose a measure based upon the fundamental theoretical concept in algorithmic information theory that provides a natural approach to the problem of evaluating $n$-dimensional complexity by using an $n$-dimensional deterministic Turing…
Measurements are shown to be processes designed to return figures: they are effective. This effectivity allows for a formalization as Turing machines, which can be described employing computation theory. Inspired in the halting problem we…
Hypercomputation or super-Turing computation is a ``computation'' that transcends the limit imposed by Turing's model of computability. The field still faces some basic questions, technical (can we mathematically and/or physically build a…
While the Ising model remains essential to understand physical phenomena, its natural connection to combinatorial reasoning makes it also one of the best models to probe complex systems in science and engineering. We bring a computational…
Bayesian statistics and Markov Chain Monte Carlo (MCMC) algorithms have found their place in the field of Cosmology. They have become important mathematical and numerical tools, especially in parameter estimation and model comparison. In…
Quantum measurement is universal for quantum computation. This universality allows alternative schemes to the traditional three-step organisation of quantum computation: initial state preparation, unitary transformation, measurement. In…
We introduce the notion of the cosmic numbers of a cosmological model, and discuss how they can be used to naturally classify models according to their ability to solve some of the problems of the standard cosmological model.
Cosmological observables are used to construct cosmological models. Since cosmological observations are limited to the light cone, a fixed number of observables (even measured to arbitrary accuracy) may not uniquely determine a cosmological…
We study the quantum measurement problem in the context of an infinite, statistically uniform space, as could be generated by eternal inflation. It has recently been argued that when identical copies of a quantum measurement system exist,…