Startseite Relations between energy complexity measures of Boolean networks and positive sensitivity of Boolean functions
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Relations between energy complexity measures of Boolean networks and positive sensitivity of Boolean functions

  • Mikhail A. Mestetskiy EMAIL logo und Mikhail S. Shupletsov
Veröffentlicht/Copyright: 9. August 2024
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Abstract

We study relationships between lower estimates for the energy complexity E(Σ), the switching complexity S(Σ) of a normalized Boolean network Σ, and the positive sensitivity ps(f) of the Boolean function f implemented by this circuit. The lower estimate E(Σ)ps(f)1m is proved for a sufficiently wide class of bases consisting of monotone Boolean functions of at most m variables, the negation gate, and the Boolean constants 0 and 1. For the switching complexity of circuits, we construct a counterexample which shows that, for the standard basis of elements of the disjunction, conjunction, and negation, there do not exist a linear (with respect to ps(f)) lower estimate for the switching complexity.


Originally published in Diskretnaya Matematika (2023) 35, №1, 71–81 (in Russian).


References

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Received: 2022-11-18
Published Online: 2024-08-09
Published in Print: 2024-08-27

© 2024 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 29.9.2025 von https://www.degruyterbrill.com/document/doi/10.1515/dma-2024-0018/html
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