Related papers: A reliable Turing machine
A computational abstract machine based on two operations: referencing and bit copying is presented. These operations are sufficient for carrying out any computation. They can be used as the primitives for a Turing-complete programming…
Neural Turing Machines (NTMs) are an instance of Memory Augmented Neural Networks, a new class of recurrent neural networks which decouple computation from memory by introducing an external memory unit. NTMs have demonstrated superior…
Wolfram [2, p. 707] and Cook [1, p. 3] claim to prove that a (2,5) Turing machine (2 states, 5 symbols) is universal, via a universal cellular automaton known as Rule 110. The first part of this paper points out a critical gap in their…
In this paper we consider the time and the crossing sequence complexities of one-tape off-line Turing machines. We show that the running time of each nondeterministic machine accepting a nonregular language must grow at least as n\log n, in…
Length generalization refers to the ability to extrapolate from short training sequences to long test sequences and is a challenge for current large language models. While prior work has proposed some architecture or data format changes to…
In this paper we investigate the computational power of a set of mobile robots with limited visibility. At each iteration, a robot takes a snapshot of its surroundings, uses the snapshot to compute a destination point, and it moves toward…
We provide partial implementations of von Neumann's universal constructor and universal copier, starting out with three types of simple building blocks using minimal assumptions. Using the same principles, we also construct Turing machines.…
According to Deutsch, a universal quantum Turing machine (UQTM) is able to perform, in repeating a fixed unitary transformation on the total system, an arbitrary unitary transformation on an arbitrary data state, by including a program as…
Overcoming the influence of noise and imperfections is a major challenge in quantum computing. Here, we present an approach based on applying a desired unitary computation in superposition between the system of interest and some auxiliary…
Molecular robotics is challenging, so it seems best to keep it simple. We consider an abstract molecular robotics model based on simple folding instructions that execute asynchronously. Turning Machines are a simple 1D to 2D folding model,…
We prove that there is no algorithm to tell whether an arbitrarily constructed Quantum Turing Machine has same time steps for different branches of computation. We, hence, can not avoid the notion of halting to be probabilistic in Quantum…
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…
Computing circuits composed of noisy logical gates and their ability to represent arbitrary Boolean functions with a given level of error are investigated within a statistical mechanics setting. Bounds on their performance, derived in the…
The effect of multiplicative noise to the Turing instability of the Brusselator system is investigated. We show that when the noise acts on both of the concentrations with the same intensities, then the Turing instability is suppressed…
Among the fundamental questions in computer science, at least two have a deep impact on mathematics. What can computation compute? How many steps does a computation require to solve an instance of the 3-SAT problem? Our work addresses the…
A catalytic Turing machine is a variant of a Turing machine in which there exists an auxiliary tape in addition to the input tape and the work tape. This auxiliary tape is initially filled with arbitrary content. The machine can read and…
This whitepaper proposes the design and adoption of a new generation of Tensor Processing Unit which has the performance of Google's TPU, yet performs operations on wide precision data. The new generation TPU is made possible by…
Foundations of the notion of quantum Turing machines are investigated. According to Deutsch's formulation, the time evolution of a quantum Turing machine is to be determined by the local transition function. In this paper, the local…
Probabilistic inference from real-time input data is becoming increasingly popular and may be one of the potential pathways at enabling cognitive intelligence. As a matter of fact, preliminary research has revealed that stochastic…
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…