A Linear Decomposition of Index Generation Functions: Optimization Using Autocorrelation Functions

Various methods exist to decompose logic functions into linear and nonlinear parts. They are used to simplify AND-OR logic circuits [3, 5, 7, 9, 22], or to simplify binary decision diagrams [4, 6, 8]. The first important observation is that the linear part can be implemented with lower cost than the non-linear part [7, 9]. To find a linear part of a decomposition, Walsh spectrum [3] and autocorrelation functions [22] are used. Since autocorrelations are invariant under a linear transformation of the input variables [10], they are useful for linear decompositions. The second important observation is that an incompletely specified function often can be represented with a fewer variables than the original number of the variables [1]. In this paper, we use linear decompositions to realize incompletely specified functions. This class of functions often appear in the practical circuits, and their cost can be reduced drastically with linear decompositions.

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