Turing Machine Model Research Articles

Refining Mark Burgin’s Case against the Church–Turing Thesis

The outputs of a Turing machine are not revealed for inputs on which the machine fails to halt. Why is an observer not allowed to see the generated output symbols as the machine operates? Building on the pioneering work of Mark Burgin, we introduce an extension of the Turing machine model with a visible output tape. As a subtle refinement to Burgin’s theory, we stipulate that the outputted symbols cannot be overwritten: at step i, the content of the output tape is a prefix of the content at step j, where i<j. Our Refined Burgin Machines (RBMs) compute more functions than Turing machines, but fewer than Burgin’s simple inductive Turing machines. We argue that RBMs more closely align with both human and electronic computers than Turing machines do. Consequently, RBMs challenge the dominance of Turing machines in computer science and beyond.

Differentiable-Decision-Tree-Based Neural Turing Machine Model Integrated Into FDTD for Implementing EM Problems

As known to all, problems consume more and more computational resources, for example, memory and time, with the gradual enhancements of both the size of the physical domain and complexity in numerical methods. Computational efficiencies have to be obviously influenced, especially for the finite-difference time-domain (FDTD) solver due to its inflexibility in discretization principle. To further overcome this problem, the neural turing machine (NTM) model, based on the differentiable decision tree (DDT), is chosen and incorporated to improve the efficiencies during the FDTD solver in our work. The DDT-based NTM model has the remarkable advantages of both trees and neural networks, which can better explain for the numerical data. Meanwhile, it has full differentiability through neural networks and can be trained by the powerful deep-learning processes. The proposed DDT-based NTM model could not only enhance both accuracy and efficiency but also successfully integrate into the FDTD solver to implement the microstrip transmission line.

Robust design strategy using a scaffold based Turing machine model--- Application to PDI based dyes

This study turns the design and screen of new compounds into a computer integer crunch of the control arrays using a scaffold based Turing machine model. If small organic fragments are stored in a fragment database (FDB) in which each fragment is labelled by an integer in an array, the position and frequency of the integer control how the fragment clicks on a scaffold (template compound). This method can robustly screen a large number of candidate fragments for solar cells and other applications such as drug design with minimal human assistance. As a proof of concept, we consider terminal imide substituents on the core perylene diimide (PDI) to develop PDI derivatives capable of absorbing UV–vis light for solar cell applications. Time dependent-density functional theory (TD-DFT) method was employed in the calculations. When the imide substituents are electron donors such as azobenzene (DPI-7), they produce a larger bathochromic shift (Δλmax) from the core DPI band position. The UV–vis absorption transitions of these DPI derivatives have more charge transfer (CT) character, as the highest occupied molecular orbitals (HOMO) are located on the fragments rather than the core DPI region. Our study presents a robust and efficient high-performance organic dye screen design strategy, and further research in DPI-based solar cell design will focus on promoting the HOMO to LUMO transitions of the optical spectra.

Pushdown Automata and Context-Free Grammars in Bisimulation Semantics

The Turing machine models an old-fashioned computer, that does not interact with the user or with other computers, and only does batch processing. Therefore, we came up with a Reactive Turing Machine that does not have these shortcomings. In the Reactive Turing Machine, transitions have labels to give a notion of interactivity. In the resulting process graph, we use bisimilarity instead of language equivalence. Subsequently, we considered other classical theorems and notions from automata theory and formal languages theory. In this paper, we consider the classical theorem of the correspondence between pushdown automata and context-free grammars. By changing the process operator of sequential composition to a sequencing operator with intermediate acceptance, we get a better correspondence in our setting. We find that the missing ingredient to recover the full correspondence is the addition of a notion of state awareness.

Efficient computations with counting functions on free groups and free monoids

We present efficient algorithms to decide whether two given counting functions on nonabelian free groups or monoids are at bounded distance from each other and to decide whether two given counting quasimorphisms on nonabelian free groups are cohomologous. We work in the multi-tape Turing machine model with nonconstant-time arithmetic operations. In the case of integer coefficients we construct an algorithm of linear time complexity (assuming that the rank is at least $3$ in the monoid case). In the case of rational coefficients we prove that the time complexity is $O(N\log N)$, where $N$ denotes the size of the input, that is, it is the same as in addition of rational numbers (implemented using the Harvey-van der Hoeven algorithm for integer multiplication). These algorithms are based on our previous work which characterizes bounded counting functions. Bibliography: 20 titles.

Testing technology for tensile properties of metal materials based on deep learning model.

The properties of metallic materials have been extensively studied, and nowadays the tensile properties testing techniques of metallic materials still have not found a suitable research method. In this paper, the neural Turing machine model is first applied to explore the tensile properties of metallic materials and its usability is demonstrated. Then the neural Turing machine model was improved. The model is then improved so that the required results can be obtained faster and more explicitly. Based on the improved Neural Turing Machine model in the exploration of tensile properties of metal materials, it was found that both H-NTM and AH-NTM have less training time than NTM. A-NTM takes more training time than AH-NTM. The improvement reduces the training time of the model. In replication, addition, and multiplication, the training time is reduced by 6.0, 8.8, and 7.3%, respectively. When the indentation interval is 0.5–0.7 mm, the error of the initial indentation data is large. The error of the tensile properties of the material obtained after removing the data at this time is significantly reduced. When the indentation interval is 0.8–1.5 mm, the stress is closer to the real value of tensile test yield strength 219.9 Mpa and tensile test tensile strength 258.8 Mpa. this paper will improve the neural Turing machine model in the exploration of metal material tensile properties testing technology has some application value.

Polynomial Multiplication over Finite Fields in Time \( O(n \log n \)

Assuming a widely believed hypothesis concerning the least prime in an arithmetic progression, we show that polynomials of degree less than \( n \) over a finite field \( \mathbb {F}_q \) with \( q \) elements can be multiplied in time \( O (n \log q \log (n \log q)) \) , uniformly in \( q \) . Under the same hypothesis, we show how to multiply two \( n \) -bit integers in time \( O (n \log n) \) ; this algorithm is somewhat simpler than the unconditional algorithm from the companion paper [ 22 ]. Our results hold in the Turing machine model with a finite number of tapes.

Incompleteness of moral choice and evolution towards fully autonomous AI

Nowadays, it is fashionable to add the attribute “with artificial intelligence” to all possible devices, platforms and machines. The problem of ethical decision-making, viewed from the perspective of computer, technical and natural sciences, lies only in the complexity of the topic. AI scientists and developers basically proceed from the Turing machine model, assuming that a machine can be constructed to resolve any problems (including ethical decision-making issues) that can mechanically calculate a particular function if this function can be put into an algorithm. Thus, ethical decision-making is conceived as an abstract concept whose manifestation does not depend on the particular physical organism in which the algorithm takes place, nor on what it is made of. Whether from photons, mechanical relays, quantum fluctuations, artificial neurons or human nerve cells. If in practice, a sufficiently complex algorithm is built, it will also exhibit sufficiently complex behavior that can be characterized as ethical in the full sense of the word. This article reflects the main argument that if a task requires some form of moral authority when it is performed by humans, its full automation, transferring the same task to autonomous machines, platforms, and AI algorithms, necessarily implies the transfer of moral competence. The question of what this competence should include presupposes empirical research and reassessing purely normative approaches in AI ethics.

A nondeterministic Turing machine variant to compute functions

Formally defining how outputs of nondeterministic computations may be combined, we propose a nondeterministic Turing machine variant to compute functions. First, we describe our inspiration, the association of a computation tree with the divide and conquer strategy. Next, we define the variant and prove its equivalence with the deterministic Turing machine model. Then, we give some examples and relate the variant to alternating, counting and metric Turing machines. After, we define the variant's time complexity classes and compare them to deterministic space, giving a new characterization of the ▪ and ▪ classes. Finally, we outline future work.

A thesis for interaction

A thesis for interaction is proposed as a foundation for theory of interaction. It formulates the minimal content computability and the maximal channel computability of all models of interaction by fixing a minimal model and a maximal model. It is shown that the interactive extensions of the recursive function model, the Turing machine model and the λ-calculus model all fall within the realm of the thesis. A major technical contribution is the design of interpreters in the maximal model for the models that fit in the thesis.

Verification of Composed Web Service Using Synthesized Nondeterministic Turing Model (SNTMM) With Multiple Tapes and Stacks

To verify the composed web services, a general view of what traits of a service need to be identified is still lacking. The existing verification model did not address any mechanism for getting alternative services if we failed to reach the desired service and partially concentrated on the reachability problem for a deterministic and non-deterministic system in sequential. This paper proposes a synthesised non-deterministic turing machine model (SNTMM) by combining the multistacked non-deterministic Turing machine (MSNTM) model and multitaped non-deterministic Turing machine (MTNTM) model to verify the composed web services for both deterministic and non-deterministic systems in parallel. The deceased transition and departed service marking algorithm have been proposed to address each participated service's reachability in composing service for all possible input in parallel. This article shows an example to demonstrate the meticulousness of the model. The experimental results show that the performance of the proposed model is measured efficiently.

Cayley polynomial–time computable groups

We propose a new generalization of Cayley automatic groups, varying the time complexity of computing multiplication, and language complexity of the normal form representatives. We first consider groups which have normal form language in the class C and multiplication by generators computable in linear time on a certain restricted Turing machine model (position–faithful one–tape). We show that many of the algorithmic properties of automatic groups are preserved, prove various closure properties, and show that the class is quite large. We then generalize to groups which have normal form language in the class C and multiplication by generators computable in polynomial time on a (standard) Turing machine. Of particular interest is when C=REG (the class of regular languages). We prove that REG–Cayley polynomial–time computable groups include all finitely generated nilpotent groups, the wreath product Z2≀Z2, and Thompson's group F.

Physical Computing: Unifying Real Number Computation to Enable Energy Efficient Computing

Physical computing unifies real value computing including analog, neuromorphic, optical, and quantum computing. Many real-valued techniques show improvements in energy efficiency, enable smaller area per computation, and potentially improve algorithm scaling. These physical computing techniques suffer from not having a strong computational theory to guide application development in contrast to digital computation’s deep theoretical grounding in application development. We consider the possibility of a real-valued Turing machine model, the potential computational and algorithmic opportunities of these techniques, the implications for implementation applications, and the computational complexity space arising from this model. These techniques have shown promise in increasing energy efficiency, enabling smaller area per computation, and potentially improving algorithm scaling.

Integer multiplication in time $O(n\mathrm{log}\, n)$

We present an algorithm that computes the product of two $n$-bit integers in $O(n \mathrm{log}\, n)$ bit operations, thus confirming a conjecture of Schönhage and Strassen from 1971. Our complexity analysis takes place in the multitape Turing machine model, with integers encoded in the usual binary representation. Central to the new algorithm is a novel ``Gaussian resampling" technique that enables us to reduce the integer multiplication problem to a collection of multidimensional discrete Fourier transforms over the complex numbers, whose dimensions are all powers of two. These transforms may then be evaluated rapidly by means of Nussbaumer's fast polynomial transforms.

A SCHEMATIC DEFINITION OF QUANTUM POLYNOMIAL TIME COMPUTABILITY

AbstractIn the past four decades, the notion of quantum polynomial-time computability has been mathematically modeled by quantum Turing machines as well as quantum circuits. This paper seeks the third model, which is a quantum analogue of the schematic (inductive or constructive) definition of (primitive) recursive functions. For quantum functions mapping finite-dimensional Hilbert spaces to themselves, we present such a schematic definition, composed of a small set of initial quantum functions and a few construction rules that dictate how to build a new quantum function from the existing ones. We prove that our schematic definition precisely characterizes all functions that can be computable with high success probabilities on well-formed quantum Turing machines in polynomial time, or equivalently uniform families of polynomial-size quantum circuits. Our new, schematic definition is quite simple and intuitive and, more importantly, it avoids the cumbersome introduction of the well-formedness condition imposed on a quantum Turing machine model as well as of the uniformity condition necessary for a quantum circuit model. Our new approach can further open a door to the descriptional complexity of quantum functions, to the theory of higher-type quantum functionals, to the development of new first-order theories for quantum computing, and to the designing of programming languages for real-life quantum computer

Analogicity in Computer Science. Methodological Analysis

Abstract Analogicity in computer science is understood in two, not mutually exclusive ways: 1) with regard to the continuity feature (of data or computations), 2) with regard to the analogousness feature (i.e. similarity between certain natural processes and computations). Continuous computations are the subject of three methodological questions considered in the paper: 1a) to what extent do their theoretical models go beyond the model of the universal Turing machine (defining digital computations), 1b) is their computational power greater than that of the universal Turing machine, 1c) under what conditions are continuous computations realizable in practice? The analogue-analogical computations lead to two other issues: 2a) in what sense and to what extent their accuracy depends on the adequacy of certain theories of empirical sciences, 2b) are there analogue-analogical computations in nature that are also continuous? The above issues are an important element of the philosophical discussion on the limitations of contemporary computer science.

Design and simulation of quantum-dot cellular automata serial decimal pipelined processor based on Turing machine model

The quantum-dot cellular automata (QCA) nanoscale computer technology is promising to overcome the limits of the microelectronic CMOS technology. Because the leading role of QCA wires, the serial data transfer/processing is preferable. The financial, Internet of Things, and control computer applications require direct processing of decimal information without representation and conversion errors. Because a QCA wire can be considered as a virtual tape with written binary symbols, a special version of Turing machine model can be used for a QCA computer implementation. Design of a novel QCA serial decimal pipelined processor based on the Turing machine model is presented. The processor uses the run-time tape reconfiguration for arithmetic processing of decimal operands encoded in the 5-bit Johnson-Mobius code. The proposed design demonstrates significant hardware simplification.

FARM: A Flexible Accelerator for Recurrent and Memory Augmented Neural Networks

Recently, Memory Augmented Neural Networks (MANN)s, a class of Deep Neural Networks (DNN)s have become prominent owing to their ability to capture the long term dependencies effectively for several Natural Language Processing (NLP) tasks. These networks augment conventional DNNs by incorporating memory and attention mechanisms external to the network to capture relevant information. Several MANN architectures have shown particular benefits in NLP tasks by augmenting an underlying Recurrent Neural Network (RNN) with external memory using attention mechanisms. Unlike conventional DNNs whose computational time is dominated by MAC operations, MANNs have more diverse behavior. In addition to MACs, the attention mechanisms of MANNs also consist of operations such as similarity measure, sorting, weighted memory access, and pair-wise arithmetic. Due to this greater diversity in operations, MANNs are not trivially accelerated by the same techniques used by existing DNN accelerators. In this work, we present an end-to-end hardware accelerator architecture, FARM, for the inference of RNNs and several variants of MANNs, such as the Differential Neural Computer (DNC), Neural Turing Machine (NTM) and Meta-learning model. FARM achieves an average speedup of 30x-190x and 80x-100x over CPU and GPU implementations, respectively. To address remaining memory bottlenecks in FARM, we then propose the FARM-PIM architecture, which augments FARM with in-memory compute support for MAC and content-similarity operations in order to reduce data traversal costs. FARM-PIM offers an additional speedup of 1.5x compared to FARM. Additionally, we consider an efficiency-oriented version of the PIM implementation, FARM-PIM-LP, that trades a 20% performance reduction relative to FARM for a 4x average power consumption reduction.

Intelligent Computing: Oxymoron?

The present paper is intended as a defense of the view that whatever makes AI so useful and successful in competition with humans, it does not have to be intelligence, at least as we use this term in the human context. After all, the question of qualification for human beings to be considered intelligent does not have a definite answer. There is not even a common agreement on whether we can identify criteria for one (general or unified) intelligence or whether we should rather consider multiple intelligences. Thus, our discussion is focusing not on a complete definition of intelligence, but only on its necessary conditions, and not on computing artefacts, but on the process of computing in its Turing Machine model. Are there any features of computing which are in contradiction with the idea of intelligence? This is the reason why the title of this paper is formulated in a negative way, with the question of whether intelligent computing is an oxymoron.

A local model of quantum Turing machines

The model of local Turing machines is introduced, including classical and quantum ones, in the framework of matrix-product states. The locality refers to the fact that at any instance of the computation the heads of a Turing machine have definite locations. The local Turing machines are shown to be equivalent to the corresponding circuit models and standard models of Turing machines by simulation methods. This work reveals the fundamental connection between tensor-network states and information processing.