Functional decomposition

Functional decomposition refers broadly to the process of resolving a functional relationship into its constituent parts in such a way that the original function can be reconstructed (i.e., recomposed) from those parts by function composition. In general, this process of decomposition is undertaken either for the purpose of gaining insight into the identity of the constituent components (which may reflect individual physical processes of interest, for example), or for the purpose of obtaining a compressed representation of the global function, a task which is feasible only when the constituent processes possess a certain level of modularity (i.e., independence or non-interaction). Interactions between the components are critical to the function of the collection. All interactions may not be observable, but possibly deduced through repetitive perception, synthesis, validation and verification of composite behavior.

For a multivariate function ${\displaystyle y=f(x_{1},x_{2},\dots ,x_{n})}$, functional decomposition generally refers to a process of identifying a set of functions ${\displaystyle \{g_{1},g_{2},\dots g_{m}\}}$ such that

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