Related papers: A Physically Universal Turing Machine
Alternatives to recurrent neural networks, in particular, architectures based on attention or convolutions, have been gaining momentum for processing input sequences. In spite of their relevance, the computational properties of these…
Coupled oscillators are being increasingly used as the basis of machine learning (ML) architectures, for instance in sequence modeling, graph representation learning and in physical neural networks that are used in analog ML devices. We…
We generalize the relativistic flux tube model for arbitrary two- or three-body systems. The spin-independent and spin-dependent contributions of the flux tube to the total Hamiltonian are computed in perturbation. In particular, we show…
We introduce the Neural Field Turing Machine (NFTM), a differentiable architecture that unifies symbolic computation, physical simulation, and perceptual inference within continuous spatial fields. NFTM combines a neural controller,…
Runge's method is a tool to figure out integral points on curves effectively in terms of height. This method has been generalised to varieties of any dimension, unfortunately its conditions of application are often too restrictive. In this…
The article introduces some ideas for solving special cases of the following problem, proposed in a somewhat generalized form by Marcus Hutter in 2000. Given two Turing machines $A$ and $C$, it is required to build a Turing machine $B$,…
Absolute combinatorial game theory was recently developed as a unifying tool for constructive/local game comparison (Larsson et al. 2018). The theory concerns {\em parental universes} of combinatorial games; standard closure properties are…
A fundamental question is whether Turing machines can model all reasoning processes. We introduce an existence principle stating that the perception of the physical existence of any Turing program can serve as a physical causation for the…
In this first of two papers, strong limits on the accuracy of physical computation are established. First it is proven that there cannot be a physical computer C to which one can pose any and all computational tasks concerning the physical…
Disentanglement is the process which transforms a state $\rho$ of two subsystems into an unentangled state, while not effecting the reduced density matrices of each of the two subsystems. Recently Terno showed that an arbitrary state cannot…
While it is well known that a Turing machine equipped with the ability to flip a fair coin cannot compute more that a standard Turing machine, we show that this is not true for a biased coin. Indeed, any oracle set $X$ may be coded as a…
We develop the formalism of universal torsors in equivariant birational geometry and apply it to produce new examples of nonbirational but stably birational actions of finite groups.
This paper introduces a class of objects called decision rules that map infinite sequences of alternatives to a decision space. These objects can be used to model situations where a decision maker encounters alternatives in a sequence such…
In the context of 'infinite-volume mixing' we prove global-local mixing for the Boole map, a.k.a. Boole transformation, which is the prototype of a non-uniformly expanding map with two neutral fixed points. Global-local mixing amounts to…
Spin models are widely studied in the natural sciences, from investigating magnetic materials in condensed matter physics to studying neural networks. Previous work has demonstrated that there exist simple classical spin models that are…
We introduce a neural stack architecture, including a differentiable parametrized stack operator that approximates stack push and pop operations for suitable choices of parameters that explicitly represents a stack. We prove the stability…
We introduce a new type of nonuniform two--way automaton that can use a different transition function for each tape square. We also enhance this model by allowing to shuffle the given input at the beginning of the computation. Then we…
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.
A Turing machine with faults, failures and recovery (TMF) is described. TMF is (weakly) non-deterministic Turing machine consisting of five semi-infinite tapes (Master Tape, Synchro Tape, Backup Tape, Backup Synchro Tape, User Tape) and…
Universality has been an important concept in computable structure theory. A class $\mathcal{C}$ of structures is universal if, informally, for any structure, of any kind, there is a structure in $\mathcal{C}$ with the same…