scholarly journals Simulations between Three Types of Networks of Splicing Processors

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1511
Author(s):  
José Ramón Sánchez Couso ◽  
José Angel Sanchez Martín ◽  
Victor Mitrana ◽  
Mihaela Păun
Keyword(s):  
Time Complexity ◽  
Computational Models ◽  
Turing Machines ◽  
Natural Phenomena ◽  
Constant Number ◽  
Computational Power ◽  
Original Network ◽  
Computational Costs ◽  
Control Degree ◽  
And Control

Networks of splicing processors (NSP for short) embody a subcategory among the new computational models inspired by natural phenomena with theoretical potential to handle unsolvable problems efficiently. Current literature considers three variants in the context of networks managed by random-context filters. Despite the divergences on system complexity and control degree over the filters, the three variants were proved to hold the same computational power through the simulations of two computationally complete systems: Turing machines and 2-tag systems. However, the conversion between the three models by means of a Turing machine is unattainable because of the huge computational costs incurred. This research paper addresses this issue with the proposal of direct and efficient simulations between the aforementioned paradigms. The information about the nodes and edges (i.e., splicing rules, random-context filters, and connections between nodes) composing any network of splicing processors belonging to one of the three categories is used to design equivalent networks working under the other two models. We demonstrate that these new networks are able to replicate any computational step performed by the original network in a constant number of computational steps and, consequently, we prove that any outcome achieved by the original architecture can be accomplished by the constructed architectures without worsening the time complexity.

scholarly journals THE ROLES OF ADVICE TO ONE-TAPE LINEAR-TIME TURING MACHINES AND FINITE AUTOMATA

2010 ◽  
Vol 21 (06) ◽  
pp. 941-962 ◽  
Author(s):  
TOMOYUKI YAMAKAMI
Keyword(s):  
Computational Models ◽  
Linear Time ◽  
Finite Automata ◽  
Probability Distributions ◽  
Finite State Automata ◽  
Turing Machines ◽  
Computational Power ◽  
Finite State

We discuss the power and limitation of various "advice," when it is given particularly to weak computational models of one-tape linear-time Turing machines and one-way finite (state) automata. Of various advice types, we consider deterministically-chosen advice (not necessarily algorithmically determined) and randomly-chosen advice (according to certain probability distributions). In particular, we show that certain weak machines can be significantly enhanced in computational power when randomized advice is provided in place of deterministic advice.

Some Assumptions about Problem Solving Representation in Turing’s Model of Intelligence

1970 ◽  
Vol 4 (2) ◽  
pp. 136-142 ◽  
Author(s):  
Raymundo Morado ◽  
Francisco Hernández-Quiroz
Keyword(s):  
Problem Solving ◽  
Computational Models ◽  
Turing Machines

Turing machines as a model of intelligence can be motivated under some assumptions, both mathematical and philosophical. Some of these are about the possibility, the necessity, and the limits of representing problem solving by mechanical means. The assumptions about representation that we consider in this paper are related to information representability and availability, processing as solving, nonessentiality of complexity issues, and finiteness, discreteness and sequentiality of the representation. We discuss these assumptions and particularly something that might happen if they were to be rejected or weakened. Tinkering with these assumptions sheds light on the import of alternative computational models.

scholarly journals The Environment Is Not A System

2018 ◽  
Vol 7 (1) ◽  
pp. 152-165
Author(s):  
Tega Brain
Keyword(s):  
Knowledge Production ◽  
Mass Extinction ◽  
Computational Models ◽  
Rapid Climate Change ◽  
The World ◽  
History Of Ecology ◽  
History Of ◽  
And Control ◽  
Systems View ◽  
Manipulation And Control

This paper considers some of the limitations and possibilities of computational models in the context of environmental inquiry, specifically exploring the modes of knowledge production that it mobilizes. Historic computational attempts to model, simulate and make predictions about environmental assemblages, both emerge from and reinforce a systems view on the world. The word eco-system itself stands as a reminder that the history of ecology is enmeshed with systems theory and presup-poses that species entanglements are operational or functional. More surreptitiously, a systematic view of the environment connotes it as bounded, knowable and made up of components operating in chains of cause and effect. This framing strongly invokes possibilities of manipulation and control and implicitly asks: what should an ecosystem be optimized for? This question is particularly relevant at a time of rapid climate change, mass extinction and, conveniently, an unprecedented surplus of computing.

Locally Recurrent Neural Networks and Their Applications

2010 ◽  
pp. 195-222
Author(s):  
Todor D. Ganchev
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Computational Models ◽  
Machine Learning Techniques ◽  
Spatial Correlations ◽  
Temporal Correlations ◽  
Learning Techniques ◽  
Locally Recurrent ◽  
The One ◽  
And Control

In this chapter we review various computational models of locally recurrent neurons and deliberate the architecture of some archetypal locally recurrent neural networks (LRNNs) that are based on them. Generalizations of these structures are discussed as well. Furthermore, we point at a number of realworld applications of LRNNs that have been reported in past and recent publications. These applications involve classification or prediction of temporal sequences, discovering and modeling of spatial and temporal correlations, process identification and control, etc. Validation experiments reported in these developments provide evidence that locally recurrent architectures are capable of identifying and exploiting temporal and spatial correlations (i.e., the context in which events occur), which is the main reason for their advantageous performance when compared with the one of their non-recurrent counterparts or other reasonable machine learning techniques.

scholarly journals Complexity-theoretic aspects of expanding cellular automata

2020 ◽  
Author(s):  
Augusto Modanese
Keyword(s):  
Cellular Automata ◽  
Polynomial Time ◽  
Time Complexity ◽  
Truth Table ◽  
Decision Problems ◽  
Turing Machines ◽  
One Dimensional ◽  
Alternative Characterization ◽  
Time Class ◽  
Theoretical Standpoint

Abstract The expanding cellular automata (XCA) variant of cellular automata is investigated and characterized from a complexity-theoretical standpoint. An XCA is a one-dimensional cellular automaton which can dynamically create new cells between existing ones. The respective polynomial-time complexity class is shown to coincide with $${\le _{tt}^p}(\textsf {NP})$$ ≤ tt p ( NP ) , that is, the class of decision problems polynomial-time truth-table reducible to problems in $$\textsf {NP}$$ NP . An alternative characterization based on a variant of non-deterministic Turing machines is also given. In addition, corollaries on select XCA variants are proven: XCAs with multiple accept and reject states are shown to be polynomial-time equivalent to the original XCA model. Finally, XCAs with alternative acceptance conditions are considered and classified in terms of $${\le _{tt}^p}(\textsf {NP})$$ ≤ tt p ( NP ) and the Turing machine polynomial-time class $$\textsf {P}$$ P .

scholarly journals Processing Information in the Clouds

Proceedings ◽  
2020 ◽  
Vol 47 (1) ◽  
pp. 25
Author(s):  
Mark Burgin ◽  
Eugene Eberbach ◽  
Rao Mikkilineni
Keyword(s):  
Artificial Intelligence ◽  
Cloud Computing ◽  
Human Brain ◽  
Incremental Learning ◽  
Computational Models ◽  
Higher Order ◽  
Turing Machines ◽  
New Paradigm ◽  
New Model ◽  
Processing Information

Cloud computing makes the necessary resources available to the appropriate computation to improve scaling, resiliency, and the efficiency of computations. This makes cloud computing a new paradigm for computation by upgrading its artificial intelligence (AI) to a higher order. To explore cloud computing using theoretical tools, we use cloud automata as a new model for computation. Higher-level AI requires infusing features of the human brain into AI systems such as incremental learning all the time. Consequently, we propose computational models that exhibit incremental learning without stopping (sentience). These features are inherent in reflexive Turing machines, inductive Turing machines, and limit Turing machines.

scholarly journals Space and time complexity for infinite time Turing machines

2020 ◽  
Vol 30 (6) ◽  
pp. 1239-1255
Author(s):  
Merlin Carl
Keyword(s):  
Time Complexity ◽  
Space Complexity ◽  
Complexity Classes ◽  
Turing Machines ◽  
Infinite Time ◽  
Space And Time ◽  
Open Questions ◽  
Separation Results ◽  
Ordinal Computability

Abstract We consider notions of space by Winter [21, 22]. We answer several open questions about these notions, among them whether low space complexity implies low time complexity (it does not) and whether one of the equalities P=PSPACE, P$_{+}=$PSPACE$_{+}$ and P$_{++}=$PSPACE$_{++}$ holds for ITTMs (all three are false). We also show various separation results between space complexity classes for ITTMs. This considerably expands our earlier observations on the topic in Section 7.2.2 of Carl (2019, Ordinal Computability: An Introduction to Infinitary Machines), which appear here as Lemma $6$ up to Corollary $9$.

scholarly journals Revisiting the simulation of quantum Turing machines by quantum circuits

2019 ◽  
Vol 475 (2226) ◽  
pp. 20180767 ◽  
Author(s):  
Abel Molina ◽  
John Watrous
Keyword(s):  
Turing Machine ◽  
Polynomial Time ◽  
Computational Models ◽  
Circuit Complexity ◽  
Simulation Method ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Turing Machines ◽  
Generated Family ◽  
Quantum Turing Machine

Yao's 1995 publication ‘Quantum circuit complexity’ in Proceedings of the 34th Annual IEEE Symposium on Foundations of Computer Science , pp. 352–361, proved that quantum Turing machines and quantum circuits are polynomially equivalent computational models: t ≥ n steps of a quantum Turing machine running on an input of length n can be simulated by a uniformly generated family of quantum circuits with size quadratic in t , and a polynomial-time uniformly generated family of quantum circuits can be simulated by a quantum Turing machine running in polynomial time. We revisit the simulation of quantum Turing machines with uniformly generated quantum circuits, which is the more challenging of the two simulation tasks, and present a variation on the simulation method employed by Yao together with an analysis of it. This analysis reveals that the simulation of quantum Turing machines can be performed by quantum circuits having depth linear in t , rather than quadratic depth, and can be extended to variants of quantum Turing machines, such as ones having multi-dimensional tapes. Our analysis is based on an extension of method described by Arright, Nesme and Werner in 2011 in Journal of Computer and System Sciences 77 , 372–378. ( doi:10.1016/j.jcss.2010.05.004 ), that allows for the localization of causal unitary evolutions.

QUANTUM COMPUTATION WITH RESTRICTED AMPLITUDES

2003 ◽  
Vol 14 (05) ◽  
pp. 853-870 ◽  
Author(s):  
HARUMICHI NISHIMURA
Keyword(s):  
Quantum Computation ◽  
Polynomial Time ◽  
Exact Algorithms ◽  
Quantum Computers ◽  
Turing Machines ◽  
Computational Power ◽  
Polynomial Time Algorithms ◽  
Exact Quantum ◽  
Bounded Error ◽  
Transition Amplitudes

In this paper, we explore the power of quantum computers with restricted transition amplitudes. In 1997 Adleman, DeMarrais, and Huang showed that quantum Turing machines (QTMs) with the amplitudes from [Formula: see text] are computationally equivalent to ones with the polynomial-time computable amplitudes as machines implementing bounded-error polynomial-time algorithms. We show that QTMs with the amplitudes from [Formula: see text] is polynomial-time equivalent to deterministic Turing machines as machines implementing exact algorithms, i.e., algorithms that output correct answers with certainty. By extending this result, it is shown that exact quantum computers with rational biased coins are equivalent to classical computers. Moreover, we discuss the computational power of exact quantum computers with multiple types of coins. We also show that, from the viewpoint of zero-error polynomial-time algorithms, [Formula: see text] is not more powerful than [Formula: see text] as the set of amplitudes taken by QTMs; however, it is sufficient to solve the factoring problem.

A FAST ALGORITHM FOR COMPUTING SAMPLE ENTROPY

2011 ◽  
Vol 03 (01n02) ◽  
pp. 167-186 ◽  
Author(s):  
YING JIANG ◽  
DONG MAO ◽  
YUESHENG XU
Keyword(s):  
Time Series ◽  
Data Structure ◽  
Fast Algorithm ◽  
Time Complexity ◽  
Computing Time ◽  
Sample Entropy ◽  
Computational Costs ◽  
Tree Data ◽  
Input Time ◽  
Tree Data Structure

Sample entropy is a widely used tool for quantifying complexity of a biological system. Computing sample entropy directly using its definition requires large computational costs. We propose a fast algorithm based on a k-d tree data structure for computing sample entropy. We prove that the time complexity of the proposed algorithm is [Formula: see text] and its space complexity is O(N log N), where N is the length of the input time series and m is the length of its pattern templates. We present a numerical experiment that demonstrates significant improvement of the proposed algorithm in computing time.

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