On the representation of multi-input systems: Computational properties of polynomial algorithms

This paper introduces a theoretical framework for characterizing and classifying simple parallel algorithms and systems with many inputs, for example an array of photoreceptors. The polynomial representation (Taylor series development) of a large class of operators is introduced and its range of validity discussed. The problems involved in the polynomial approximation of systems are also briefly reviewed. Symmetry properties of the input-output map and their implications for the system structure (i.e. its kernels) are studied. Finally, the computational properties of polynomial mappings are characterized.

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