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Decomposition of reversible logic function based on cube-reordering

Lukac Martin (Graduate School of Information Sciences, Tohoku University, Sendai, Japan)
Kameyama Michitaka (Graduate School of Information Sciences, Tohoku University, Sendai, Japan)
Perkowski Marek (Department of Computer and Electrical Engineering, Portland State University, Portland, USA)
Kerntopf Pawel (Institute of Computer Science, Warsaw University of Technology, Warsaw, Poland + Department of Theoretical Physics and Informatics, University of Lodz, Lodz, Poland)

We present a novel approach to the synthesis of incompletely specified reversible logic functions. The method is based on cube grouping; the first step of the synthesis method analyzes the logic function and generates groupings of same cubes in such a manner that multiple sub-functions are realized by a single Toffoli gate. This process also reorders the function in such a manner that not only groups of similarly defined cubes are joined together but also don’t care cubes. The proposed method is verified on standard benchmarks for both reversible and irreversible logic functions. The obtained results show that for functions with a significant portion of don’t cares the proposed method outperforms previously proposed synthesis methods.

Keywords: reversible logic synthesis, Toffoli gates, cube reordering, incompletely specified functions