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Minimizing Binary Decision Diagrams for Systems of Incompletely Defined Boolean Functions Using Algebraic Cofactor Expansions

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Abstract

The main optimization criterion in the synthesis of combinational circuits from library logic elements is the number of literals in algebraic multilevel representations of systems of fully defined Boolean functions. After obtaining the binary decision diagrams of the initial systems of incompletely defined (partial) Boolean functions, it is proposed to perform additional logical optimization based on the search for algebraic representations of partial subfunctions (cofactors) of one level of a binary decision diagram in the form of a disjunction or conjunction of other subfunctions of the given level of a binary decision diagram. The proposed method makes it possible to reduce the number of literals by replacing the Shannon expansion (decomposition) formulas with simpler formulas in the transition to a multilevel representation of a system of completely defined functions, according to which a combinational logic circuit is synthesized.

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  1. United Institute of Informatics Problems, National Academy of Sciences of Belarus, 220012, Minsk, Belarus

    P. N. Bibilo

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Bibilo, P.N. Minimizing Binary Decision Diagrams for Systems of Incompletely Defined Boolean Functions Using Algebraic Cofactor Expansions. J. Comput. Syst. Sci. Int. 61, 539–566 (2022). https://doi.org/10.1134/S1064230722030029

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