Linear decomposition of mu1tioutput Boolean functions represented in SOP form

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    The paper deals with a problem of linear decomposition of multi-output logic functions. The decomposed system consists of linear function followed by nonlinear function of minimal realization cost in tenns of number of terms and literals. Obtaining the linear function involves calculation of the autocorrelation function and construction of the linear transform matrix. The complexity of determining the linear ftnction makes this approach inapplicable for systems of large number of inputs when represented by truth table or binary decision diagrams. The paper considers the case when the given logic function of many input variables is defined in a form of Sum of Products (SOP) or as a set of disjoint cubes. For this case, the suggested linearization technique combines a new method for calculation of the autocorrelation function on the disjoint cubes domain, with a simplified procedure for construction of the linear part by representing it as a superposition of linear transfonns of a special form. Experimental benchmark results allow comparing the proposed technique with known linearization methods, and show the high efficiency of the proposed approach.

    Original languageEnglish
    Pages (from-to)219-226
    Number of pages8
    JournalWSEAS Transactions on Circuits and Systems
    Issue number2
    StatePublished - Feb 2006


    • Autocorrelation
    • Complexity
    • Disjoint cubes
    • K-procedure
    • Linear decomposition
    • Logic design
    • Spectral technique
    • Walsh transform
    • Wiener-Khinchin


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