Abstract
We say that a reversible boolean function on n bits has alternation depth \(d\) if it can be written as the sequential composition of \(d\) reversible boolean functions, each of which acts only on the top \(n-1\) bits or on the bottom \(n-1\) bits. We show that every reversible boolean function of \(n\geqslant 4\) bits has alternation depth 9.
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Selinger, P. (2016). A Finite Alternation Result for Reversible Boolean Circuits. In: Devitt, S., Lanese, I. (eds) Reversible Computation. RC 2016. Lecture Notes in Computer Science(), vol 9720. Springer, Cham. https://doi.org/10.1007/978-3-319-40578-0_20
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DOI: https://doi.org/10.1007/978-3-319-40578-0_20
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