The infinity computer vs. symbolic computations: First steps in comparison

2020 ◽  
Author(s):  
Marat S. Mukhametzhanov ◽  
Yaroslav D. Sergeyev
Keyword(s):  
Symbolic Computations ◽  
Infinity Computer

Symbolic Computations

1998 ◽  
pp. 149-162
Author(s):  
Darren Redfern ◽  
Colin Campbell
Keyword(s):  
Symbolic Computations

Redesigning Parallel Symbolic Computations Packages

2007 ◽  
Author(s):  
Georgiana Macariu ◽  
Marc Frincu ◽  
Alexandru Carstea ◽  
Dana Petcu ◽  
Andrei Eckstein
Keyword(s):  
Symbolic Computations

Susycal - Symbolic computations in supersymmetric theories

1990 ◽  
Vol 58 (1-2) ◽  
pp. 89-104 ◽  
Author(s):  
T. Kreuzberger ◽  
W. Kummer ◽  
M. Schweda
Keyword(s):  
Symbolic Computations ◽  
Supersymmetric Theories

Chapter 9. Spike-Based Symbolic Computations on Bit Strings and Numbers

2021 ◽  
Author(s):  
Ceca Kraišniković ◽  
Wolfgang Maass ◽  
Robert Legenstein
Keyword(s):  
Neural Networks ◽  
Energy Efficient ◽  
Learning Rule ◽  
Spiking Neural Networks ◽  
New Paradigm ◽  
Symbolic Computations ◽  
Neuromorphic Hardware ◽  
State Of Research ◽  
Higher Cognitive Functions ◽  
The Brain

The brain uses recurrent spiking neural networks for higher cognitive functions such as symbolic computations, in particular, mathematical computations. We review the current state of research on spike-based symbolic computations of this type. In addition, we present new results which show that surprisingly small spiking neural networks can perform symbolic computations on bit sequences and numbers and even learn such computations using a biologically plausible learning rule. The resulting networks operate in a rather low firing rate regime, where they could not simply emulate artificial neural networks by encoding continuous values through firing rates. Thus, we propose here a new paradigm for symbolic computation in neural networks that provides concrete hypotheses about the organization of symbolic computations in the brain. The employed spike-based network models are the basis for drastically more energy-efficient computer hardware – neuromorphic hardware. Hence, our results can be seen as creating a bridge from symbolic artificial intelligence to energy-efficient implementation in spike-based neuromorphic hardware.

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