scholarly journals The computing power of Turing machine based on quantum logic

10.29007/k8cb ◽  
2018 ◽  
Author(s):  
Yun Shang ◽  
Xian Lu ◽  
Ruqian Lu
Keyword(s):  
Quantum Logic ◽  
Turing Machine ◽  
Turing Machines ◽  
Computational Power ◽  
Orthomodular Lattices ◽  
Locally Finite ◽  
Computing Power ◽  
Truth Value ◽  
Quantum Language

Turing machines based on quantum logic can solve undecidableproblems. In this paper we will give recursion-theoreticalcharacterization of the computational power of this kind of quantumTuring machines. In detail, for the unsharp case, it is proved that&#931<sup>0</sup><sub>1</sub>&#8746&#928<sup>0</sup><sub>1</sub>&#8838L<sup>T</sup><sub>d</sub>(&#949,&#931)(L<sup>T</sup><sub>w</sub>(&#949,&#931))&#8838&#928<sup>0</sup><sub>2</sub>when the truth value lattice is locally finite and the operation &#8743is computable, whereL<sup>T</sup><sub>d</sub>(&#949,&#931)(L<sup>T</sup><sub>w</sub>(&#949,&#931))denotes theclass of quantum language accepted by these Turing machine indepth-first model (respectively, width-first model);for the sharp case, we can obtain similar results for usual orthomodular lattices.

scholarly journals The Computational Power of Interactive Recurrent Neural Networks

2012 ◽  
Vol 24 (4) ◽  
pp. 996-1019 ◽  
Author(s):  
Jérémie Cabessa ◽  
Hava T. Siegelmann
Keyword(s):  
Neural Networks ◽  
Turing Machine ◽  
Recurrent Neural Networks ◽  
Turing Machines ◽  
Computational Power ◽  
Machine Model ◽  
Computational Framework

In classical computation, rational- and real-weighted recurrent neural networks were shown to be respectively equivalent to and strictly more powerful than the standard Turing machine model. Here, we study the computational power of recurrent neural networks in a more biologically oriented computational framework, capturing the aspects of sequential interactivity and persistence of memory. In this context, we prove that so-called interactive rational- and real-weighted neural networks show the same computational powers as interactive Turing machines and interactive Turing machines with advice, respectively. A mathematical characterization of each of these computational powers is also provided. It follows from these results that interactive real-weighted neural networks can perform uncountably many more translations of information than interactive Turing machines, making them capable of super-Turing capabilities.

ON THE POWER OF ONE-WAY GLOBALLY DETERMINISTIC SYNCHRONIZED ALTERNATING TURING MACHINES AND MULTIHEAD AUTOMATA

1995 ◽  
Vol 06 (04) ◽  
pp. 431-446 ◽  
Author(s):  
ANNA SLOBODOVÁ
Keyword(s):  
Turing Machine ◽  
Simple Form ◽  
Space Complexity ◽  
Complexity Classes ◽  
Turing Machines ◽  
Computational Power ◽  
Parallel Processes ◽  
Open Questions ◽  
The One ◽  
Alternating Turing Machines

The alternating model augmented by a special simple form of communication among parallel processes—the so-called synchronized alternating (SA) model, provides (besides others) nice characterizations of the space complexity classes defined by nondeterministic Turing machines. The model investigated in this paper — globally deterministic synchronized alternating (GDSA) model—is obtained by a feasible restriction of nondeterminism in SA. It is known that it characterizes the deterministic counterparts of the nondeterministic space classes characterized by the SA model. In the paper we resume in the investigation of GDSA solving the open questions about the computational power of the one-way GDSA models. It is known that in the case of space-bounded Turing machine and multihead automata, the one-way SA models are equivalent to their two-way counterparts. We show that the same holds for GDSA models. The results contribute to the knowledge about the model and imply new characterizations of the deterministic space complexity classes.

scholarly journals An Informal Arithmetical Approach to Computability and Computation, II

1964 ◽  
Vol 7 (2) ◽  
pp. 183-200 ◽  
Author(s):  
Z.A. Melzak
Keyword(s):  
Turing Machine ◽  
Turing Machines ◽  
Symbol Space ◽  
Computing Device ◽  
Computing Power ◽  
Adequate Supply ◽  
Universal Turing Machine ◽  
At Will

In the first part of this paper [l] there was introduced a hypothetical computing device, the Q-machine. It was derived by abstracting from the process of calculating carried out by a man on his fingers, assuming an adequate supply of hands and the ability to grow fingers at will. The Q-machine was shown to be equal in computing power to a universal Turing machine. That is, the Q-machine could compute any number regarded as computable by any theory of computability developed so far. It may be recalled here that Turing machines were obtained by Turing [2] by abstracting from the process of calculating carried out by a man on some concrete 'symbol space' (tape, piece of paper, blackboard) by means of fixed but arbitrary symbols. Hence the contrast between the Q-machine and the Turing machines is that between arithmetical manipulation of counters and logical manipulation of symbols. In particular, one might say, loosely, that in a Turing machine, as in arithmetic, numbers are represented by signs whereas in the Q-machine, as on a counting frame, numbers represent themselves.

scholarly journals Computing power of Turing machines in the framework of unsharp quantum logic

2015 ◽  
Vol 598 ◽  
pp. 2-14
Author(s):  
Yun Shang ◽  
Xian Lu ◽  
Ruqian Lu
Keyword(s):  
Quantum Logic ◽  
Turing Machines ◽  
Computing Power

scholarly journals On Turing Machines Deciding According to the Shortest Computations

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 304
Author(s):  
Florin Manea
Keyword(s):  
Computational Complexity ◽  
Turing Machine ◽  
Polynomial Time ◽  
Point Of View ◽  
The Other ◽  
Input Word ◽  
Turing Machines ◽  
Other Hand

In this paper we propose and analyse from the computational complexity point of view several new variants of nondeterministic Turing machines. In the first such variant, a machine accepts a given input word if and only if one of its shortest possible computations on that word is accepting; on the other hand, the machine rejects the input word when all the shortest computations performed by the machine on that word are rejecting. We are able to show that the class of languages decided in polynomial time by such machines is PNP[log]. When we consider machines that decide a word according to the decision taken by the lexicographically first shortest computation, we obtain a new characterization of PNP. A series of other ways of deciding a language with respect to the shortest computations of a Turing machine are also discussed.

scholarly journals Networks of Uniform Splicing Processors: Computational Power and Simulation

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1217
Author(s):  
Sandra Gómez-Canaval ◽  
Victor Mitrana ◽  
Mihaela Păun ◽  
José Angel Sanchez Martín ◽  
José Ramón Sánchez Couso
Keyword(s):  
Turing Machine ◽  
General Model ◽  
Network Size ◽  
Software Implementation ◽  
Turing Machines ◽  
Computational Power ◽  
Input And Output ◽  
New Variant ◽  
Theoretical Results

We investigated the computational power of a new variant of network of splicing processors, which simplifies the general model such that filters remain associated with nodes but the input and output filters of every node coincide. This variant, called network of uniform splicing processors, might be implemented more easily. Although the communication in the new variant seems less powerful, the new variant is sufficiently powerful to be computationally complete. Thus, nondeterministic Turing machines were simulated by networks of uniform splicing processors whose size depends linearly on the alphabet of the Turing machine. Furthermore, the simulation was time efficient. We argue that the network size can be decreased to a constant, namely six nodes. We further show that networks with only two nodes are able to simulate 2-tag systems. After these theoretical results, we discuss a possible software implementation of this model by proposing a conceptual architecture and describe all its components.

Turing Machines Based on Quantum Logic and Their Universality

2012 ◽  
Vol 35 (7) ◽  
pp. 1407 ◽  
Author(s):  
Yong-Ming LI ◽  
Ping LI
Keyword(s):  
Quantum Logic ◽  
Turing Machines

Intersections of quotient rings and Prüfer v-multiplication domains

2016 ◽  
Vol 15 (08) ◽  
pp. 1650149 ◽  
Author(s):  
Said El Baghdadi ◽  
Marco Fontana ◽  
Muhammad Zafrullah
Keyword(s):  
Integral Domain ◽  
Algebraic Approach ◽  
Quotient Field ◽  
Topological Characterization ◽  
Locally Finite ◽  
Star Operation ◽  
Star Operations ◽  
Quotient Rings ◽  
Special Case

Let [Formula: see text] be an integral domain with quotient field [Formula: see text]. Call an overring [Formula: see text] of [Formula: see text] a subring of [Formula: see text] containing [Formula: see text] as a subring. A family [Formula: see text] of overrings of [Formula: see text] is called a defining family of [Formula: see text], if [Formula: see text]. Call an overring [Formula: see text] a sublocalization of [Formula: see text], if [Formula: see text] has a defining family consisting of rings of fractions of [Formula: see text]. Sublocalizations and their intersections exhibit interesting examples of semistar or star operations [D. D. Anderson, Star operations induced by overrings, Comm. Algebra 16 (1988) 2535–2553]. We show as a consequence of our work that domains that are locally finite intersections of Prüfer [Formula: see text]-multiplication (respectively, Mori) sublocalizations turn out to be Prüfer [Formula: see text]-multiplication domains (PvMDs) (respectively, Mori); in particular, for the Mori domain case, we reobtain a special case of Théorème 1 of [J. Querré, Intersections d’anneaux intègers, J. Algebra 43 (1976) 55–60] and Proposition 3.2 of [N. Dessagnes, Intersections d’anneaux de Mori — exemples, Port. Math. 44 (1987) 379–392]. We also show that, more than the finite character of the defining family, it is the finite character of the star operation induced by the defining family that causes the interesting results. As a particular case of this theory, we provide a purely algebraic approach for characterizing P vMDs as a subclass of the class of essential domains (see also Theorem 2.4 of [C. A. Finocchiaro and F. Tartarone, On a topological characterization of Prüfer [Formula: see text]-multiplication domains among essential domains, preprint (2014), arXiv:1410.4037]).

Analyzing self-★ island-based memetic algorithms in heterogeneous unstable environments

2016 ◽  
Vol 32 (5) ◽  
pp. 676-692 ◽  
Author(s):  
Rafael Nogueras ◽  
Carlos Cotta
Keyword(s):  
Memetic Algorithm ◽  
Memetic Algorithms ◽  
Population Based ◽  
Self Healing ◽  
Computational Power ◽  
Ability To Work ◽  
Computing Power ◽  
Simulated Environment ◽  
Computational Resources ◽  
Better Than

Computational environments emerging from the pervasiveness of networked devices offer a plethora of opportunities and challenges. The latter arise from their dynamic, inherently volatile nature that tests the resilience of algorithms running on them. Here we consider the deployment of population-based optimization algorithms on such environments, using the island model of memetic algorithms for this purpose. These memetic algorithms are endowed with self-★ properties that give them the ability to work autonomously in order to optimize their performance and to react to the instability of computational resources. The main focus of this work is analyzing the performance of these memetic algorithms when the underlying computational substrate is not only volatile but also heterogeneous in terms of the computational power of each of its constituent nodes. To this end, we use a simulated environment that allows experimenting with different volatility rates and heterogeneity scenarios (that is, different distributions of computational power among computing nodes), and we study different strategies for distributing the search among nodes. We observe that the addition of self-scaling and self-healing properties makes the memetic algorithm very robust to both system instability and computational heterogeneity. Additionally, a strategy based on distributing single islands on each computational node is shown to perform globally better than placing many such islands on each of them (either proportionally to their computing power or subject to an intermediate compromise).

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