Turing Universality of Step-Wise and Stage Assembly at Temperature 1

2012 ◽  
pp. 1-11 ◽  
Author(s):  
Bahar Behsaz ◽  
Ján Maňuch ◽  
Ladislav Stacho
Keyword(s):  
Turing Universality

scholarly journals Novel Numerical Spiking Neural P Systems with a Variable Consumption Strategy

Processes ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 549
Author(s):  
Xiu Yin ◽  
Xiyu Liu ◽  
Minghe Sun ◽  
Qianqian Ren
Keyword(s):  
Production Functions ◽  
P Systems ◽  
P System ◽  
Computing Device ◽  
Spiking Neural P Systems ◽  
Distributed Parallel Computing ◽  
Production Values ◽  
Novel Variant ◽  
Turing Universality ◽  
Variable Consumption

A novel variant of NSN P systems, called numerical spiking neural P systems with a variable consumption strategy (NSNVC P systems), is proposed. Like the spiking rules consuming spikes in spiking neural P systems, NSNVC P systems introduce a variable consumption strategy by modifying the form of the production functions used in NSN P systems. Similar to the delay feature of the spiking rules, NSNVC P systems introduce a postponement feature into the production functions. The execution of the production functions in NSNVC P systems is controlled by two, i.e., polarization and threshold, conditions. Multiple synaptic channels are used to transmit the charges and the production values in NSNVC P systems. The proposed NSNVC P systems are a type of distributed parallel computing models with a directed graphical structure. The Turing universality of the proposed NSNVC P systems is proved as number generating/accepting devices. Detailed descriptions are provided for NSNVC P systems as number generating/accepting devices. In addition, a universal NSNVC P system with 66 neurons is constructed as a function computing device.

Spiking Neural P Systems with Extended Channel Rules

2020 ◽  
Vol 31 (01) ◽  
pp. 2050049 ◽  
Author(s):  
Zeqiong Lv ◽  
Tingting Bao ◽  
Nan Zhou ◽  
Hong Peng ◽  
Xiangnian Huang ◽  
...  
Keyword(s):  
Parallel Computing ◽  
Control Mechanism ◽  
P Systems ◽  
Multiple Channels ◽  
Spiking Neural P Systems ◽  
Distributed Parallel Computing ◽  
New Variant ◽  
New Type ◽  
Turing Universality ◽  
Computing Models

This paper discusses a new variant of spiking neural P systems (in short, SNP systems), spiking neural P systems with extended channel rules (in short, SNP–ECR systems). SNP–ECR systems are a class of distributed parallel computing models. In SNP–ECR systems, a new type of spiking rule is introduced, called ECR. With an ECR, a neuron can send the different numbers of spikes to its subsequent neurons. Therefore, SNP–ECR systems can provide a stronger firing control mechanism compared with SNP systems and the variant with multiple channels. We discuss the Turing universality of SNP–ECR systems. It is proven that SNP–ECR systems as number generating/accepting devices are Turing universal. Moreover, we provide a small universal SNP–ECR system as function computing devices.

TURING UNIVERSALITY OF RECURSIVE PATTERNS FOR PARALLEL PROGRAMMING

2002 ◽  
Vol 12 (02) ◽  
pp. 229-246 ◽  
Author(s):  
JÖRG FISCHER ◽  
SERGEI GORLATCH
Keyword(s):  
Parallel Programming ◽  
Numerical Integration ◽  
Programming Language ◽  
Expressive Power ◽  
Recursive Functions ◽  
Partial Recursive Functions ◽  
Turing Universality ◽  
Primitive Recursive ◽  
The Way

Dijkstra's famous thesis "goto considered harmful", which paved the way for structured programming, was formally substantiated by the result of Böhm and Jacopini on the Turing universality of the three well-known basic programming constructs. We argue for a similar ideal in parallel programming — "send-receive considered harmful" — i.e. abandoning explicit send-receive statements between processors and expressing programs using a restricted set of parallel constructs. We deal with recursive patterns of parallelism, represented formally as morphisms in a suitable calculus. The aim of this paper is to study the expressive power of two morphisms – catamorphisms and anamorphisms. For a restricted program calculus based on these morphisms, we constructively prove two formal results, whose pragmatic message is: (1) A programming language based on catamorphisms is computationally equivalent to the class of primitive recursive functions; (2) A programming language based on both catamorphisms and anamorphisms is equivalent to the class of partial recursive functions and is therefore Turing-universal. We present a case study on numerical integration, demonstrating the expressive power of ana- and catamorphisms for parallel programming.

Nine switch-affine neurons suffice for Turing universality

1999 ◽  
Vol 12 (4-5) ◽  
pp. 593-600 ◽  
Author(s):  
H.T. Siegelmann ◽  
M. Margenstern
Keyword(s):  
Turing Universality

scholarly journals Turing Universality of Weighted Spiking Neural P Systems with Anti-spikes

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Qianqian Ren ◽  
Xiyu Liu ◽  
Minghe Sun
Keyword(s):  
P Systems ◽  
P System ◽  
Number Generator ◽  
Working Process ◽  
Computing Device ◽  
Spiking Neural P Systems ◽  
Turing Universality

Weighted spiking neural P systems with anti-spikes (AWSN P systems) are proposed by adding anti-spikes to spiking neural P systems with weighted synapses. Anti-spikes behave like spikes of inhibition of communication between neurons. Both spikes and anti-spikes are used in the rule expressions. An illustrative example is given to show the working process of the proposed AWSN P systems. The Turing universality of the proposed P systems as number generating and accepting devices is proved. Finally, a universal AWSN P system having 34 neurons is proved to work as a function computing device by using standard rules, and one having 30 neurons is proved to work as a number generator.

scholarly journals Intrinsic universality and the computational power of self-assembly

2015 ◽  
Vol 373 (2046) ◽  
pp. 20140214 ◽  
Author(s):  
Damien Woods
Keyword(s):  
Self Assembly ◽  
Theoretical Models ◽  
Assembly Model ◽  
Tile Assembly Model ◽  
Intrinsic Universality ◽  
Large Structures ◽  
Large Numbers ◽  
Tile Assembly ◽  
Turing Universality ◽  
Future Work

Molecular self-assembly, the formation of large structures by small pieces of matter sticking together according to simple local interactions, is a ubiquitous phenomenon. A challenging engineering goal is to design a few molecules so that large numbers of them can self-assemble into desired complicated target objects. Indeed, we would like to understand the ultimate capabilities and limitations of this bottom-up fabrication process. We look to theoretical models of algorithmic self-assembly, where small square tiles stick together according to simple local rules in order to carry out a crystal growth process. In this survey, we focus on the use of simulation between such models to classify and separate their computational and expressive powers. Roughly speaking, one model simulates another if they grow the same structures, via the same dynamical growth processes. Our journey begins with the result that there is a single intrinsically universal tile set that, with appropriate initialization and spatial scaling, simulates any instance of Winfree's abstract Tile Assembly Model. This universal tile set exhibits something stronger than Turing universality: it captures the geometry and dynamics of any simulated system in a very direct way. From there we find that there is no such tile set in the more restrictive non-cooperative model, proving it weaker than the full Tile Assembly Model. In the two-handed model, where large structures can bind together in one step, we encounter an infinite set of infinite hierarchies of strictly increasing simulation power. Towards the end of our trip, we find one tile to rule them all: a single rotatable flipable polygonal tile that simulates any tile assembly system. We find another tile that aperiodically tiles the plane (but with small gaps). These and other recent results show that simulation is giving rise to a kind of computational complexity theory for self-assembly. It seems this could be the beginning of a much longer journey, so directions for future work are suggested.

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