Functional decomposition
Also, functional decomposition may result in 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).
Consider the particular case of "northbound traffic on the West Side Highway."
all these other secondary variables are not directly relevant to the West Side Highway traffic.
Processes related to functional decomposition are prevalent throughout the fields of knowledge representation and machine learning.
Hierarchical model induction techniques such as Logic circuit minimization, decision trees, grammatical inference, hierarchical clustering, and quadtree decomposition are all examples of function decomposition.
Many statistical inference methods can be thought of as implementing a function decomposition process in the presence of noise; that is, where functional dependencies are only expected to hold approximately.
In practical scientific applications, it is almost never possible to achieve perfect functional decomposition because of the incredible complexity of the systems under study.
This complexity is manifested in the presence of "noise," which is just a designation for all the unwanted and untraceable influences on our observations.
However, while perfect functional decomposition is usually impossible, the spirit lives on in a large number of statistical methods that are equipped to deal with noisy systems.
As an example, Bayesian network methods attempt to decompose a joint distribution along its causal fault lines, thus "cutting nature at its seams".
The essential motivation behind these methods is again that within most systems (natural or artificial), relatively few components/events interact with one another directly on equal footing.
There is thus a notion of "causal proximity" in physical systems under which variables naturally precipitate into small clusters.
Identifying these clusters and using them to represent the joint provides the basis for great efficiency of storage (relative to the full joint distribution) as well as for potent inference algorithms.
Functional Decomposition is a design method intending to produce a non-implementation, architectural description of a computer program.
The software architect first establishes a series of functions and types that accomplishes the main processing problem of the computer program, decomposes each to reveal common functions and types, and finally derives Modules from this activity.
The input signal to an LTI system can be expressed as a function,
can be decomposed into a linear combination of other functions, called component signals: Here,
This decomposition aids in analysis, because now the output of the system can be expressed in terms of the components of the input.
, which can be expressed as: In other words, the system can be seen as acting separately on each of the components of the input signal.
This exercise forces each part of the system to have a pure function.
When a system is designed as pure functions, they can be reused, or replaced.
A usual side effect is that the interfaces between blocks become simple and generic.
One might functionally decompose this into speakers, amplifier, a tape deck and a front panel.
