Polynomial expansion of symmetric boolean functions by the table method
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The proposed method for polynomial expansion of SBF based on construction of the triangular tableTn(π(F)) of local codes of its derivatives has the lowest computational complexity among known methods. Constructing the table only once, the method easily determines all the “residual” functions ϑ rl km for various expansion parametersk andm.
Another advantage of the method is its applicability for polynomial expansion of arbitrary BF and partially symmetric BF. In this case, the base of the “triangle” is the truth table of the arbitrary BF or the local code (including convolved local code) of the partially symmetric BF.
The method can be successfully used for the synthesis of a wide class of digital networks.
KeywordsOperating System Artificial Intelligence Computational Complexity System Theory Boolean Function
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