It consists of elementary transformations that represent a generalized inversion into a four-dimensional hypersphere:
2.
An elementary transformation of a word w \ in G consists of inserting or deleting a part of the form aa ^ {-1 } with a \ in S ^ { \ pm }.
3.
Although such complex edit operators can be defined in terms of more elementary transformations, their use allows finer parameterization of the cost function c when the operator is cheaper than the sum of its constituents.
4.
Two words w _ 1 and w _ 2 are equivalent, w _ 1 \ equiv w _ 2, if there is a chain of elementary transformations leading from w _ 1 to w _ 2.
5.
Indeed a simple inspection of the graph readily suggests the different steps of the reduction which are carried out by elementary transformations, by loop elimination, or by the use of a reduction formula . | Robichaud | Signal flow graphs and applications, 1962 }}
6.
The elementary transformations [ defined by Robichaud in his Figure 7.2, p . 184 ] and the loop reduction permit the elimination of any node " j " of the graph by the " reduction formula " : [ described in Robichaud's Equation 7-1 ].
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