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On the respresentation of multi-input systems: computational properties of polynomial algorithms
Biological Cybernetics
|January 1, 1980
Summary
This study presents a theoretical framework for classifying parallel algorithms and systems with multiple inputs using polynomial representations. It analyzes symmetry properties and computational characteristics of these systems for better understanding and application.
Area of Science:
- Theoretical Computer Science
- Algorithm Analysis
- System Classification
Background:
- Characterizing complex systems with numerous inputs, such as photoreceptor arrays, is challenging.
- Existing methods for approximating system behavior have limitations.
Purpose of the Study:
- To introduce a novel theoretical framework for classifying simple parallel algorithms and systems.
- To explore the use of polynomial representation for analyzing system operators.
- To investigate the impact of symmetry properties on system structure and computational properties.
Main Methods:
- Development of a polynomial representation (Taylor series) for operators.
- Analysis of symmetry properties of input-output maps.
- Characterization of computational properties of polynomial mappings.
Main Results:
- A valid theoretical framework for classifying parallel systems with many inputs is established.
- The polynomial representation is shown to be effective for a broad class of operators.
- Symmetry properties are linked to the underlying system structure and kernels.
- Computational properties of polynomial mappings are clearly defined.
Conclusions:
- The proposed framework offers a systematic approach to understanding and classifying parallel systems.
- Polynomial approximation provides a powerful tool for analyzing complex system behaviors.
- Symmetry analysis is crucial for deciphering system structure and function.
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