Related papers: Unconventional Universal Computation in Babbage's …

We show in this article that uncomputability is also a relative property of subrecursive classes built on a recursive relative incompressible function, which acts as a higher-order "yardstick" of irreducible information for the respective…

A major limitation of exact inference algorithms for probabilistic graphical models is their extensive memory usage, which often puts real-world problems out of their reach. In this paper we show how we can extend inference algorithms,…

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 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…

This work studies some aspects of the computational power of fully asynchronous cellular automata (ACA). We deal with some notions of simulation between ACA and Turing Machines. In particular, we characterize the updating sequences…

Deutsch, Feynman, and Manin viewed quantum computing as a kind of universal physical simulation procedure. Much of the writing about quantum Turing machines has shown how these machines can simulate an arbitrary unitary transformation on a…

Addressing machines have been introduced as a formalism to construct models of the pure, untyped lambda-calculus. We extend the syntax of their programs by adding instructions for executing arithmetic operations on natural numbers, and…

In this paper, we analyze the problem of finding the minimum dimension $n$ such that a closed-form analytic map/ordinary differential equation can simulate a Turing machine over $\mathbb{R}^{n}$ in a way that is robust to perturbations. We…

This paper presents an algebraic theory of instruction sequences with instructions for Turing tapes as basic instructions, the behaviours produced by the instruction sequences concerned under execution, and the interaction between such…

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…

External neural memory structures have recently become a popular tool for algorithmic deep learning (Graves et al. 2014, Weston et al. 2014). These models generally utilize differentiable versions of traditional discrete memory-access…

A variant of Turing machines is introduced where the tape is replaced by a single tree which can be manipulated in a style akin to purely functional programming. This yields two benefits: first, the extra structure on the tape can be…

We propose to implement tunable interfaces for realizing universal quantum computation with topological qubits. One interface is between the topological and superconducting qubits, which can realize arbitrary single-qubit gate on the…

We introduce differentiable indirection -- a novel learned primitive that employs differentiable multi-scale lookup tables as an effective substitute for traditional compute and data operations across the graphics pipeline. We demonstrate…

An explicit lattice realization of a non-Abelian topological memory is presented. The correspondence between logical and physical states is seen directly by use of the stabilizer formalism. The resilience of the encoded states against…

This study presents a roadmap towards utilizing a single arbitrary gate for universal quantum computing. Since two decades ago, it has been widely accepted that almost any single arbitrary gate with qubit number $>2$ is universal. Utilizing…

Many unconventional computing models, including some that appear to be quite different from traditional ones such as Turing machines, happen to characterise either the complexity class P or PSPACE when working in deterministic polynomial…

Deep Neural Networks have been found vulnerable re-cently. A kind of well-designed inputs, which called adver-sarial examples, can lead the networks to make incorrectpredictions. Depending on the different scenarios, goalsand capabilities,…

This report presents three proofs showing that idealized architectures capable of navigation guided by allocentric maps with landmark structure can be computationally universal. The navigation may occur either online (in the environment) or…

The classical lambda calculus may be regarded both as a programming language and as a formal algebraic system for reasoning about computation. It provides a computational model equivalent to the Turing machine, and continues to be of…