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Analysis of Boolean Logic Gates Logical Complexity for Use with Spiking Memristor Gates

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  • First Online:
Unconventional Computation and Natural Computation (UCNC 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9726))

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Abstract

2-Bit Boolean logical operations have been considered before, however, the focus has always been on the AND, OR, NOT, NAND and NOR gates that are of use in traditional electronics. The memristor tends to require implication and similar logics, which can be considered as sequential logics, especially when used with spiking memristor gates. Here we introduce the concept of logical efficiency based on how many differentiable operations exist in a truth table, and sequence sensitive gates (e.g. IMP) are found to have a higher logical efficiency. We propose an ideal gate which is both functionally complete and maximally logically efficient and demonstrate that it does not exist in 2-bit binary gates, but can exist in trinary. We propose that this novel theoretical approach will aid the building of neuromorphic computers that will be highly efficient, powerful and resilient.

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Notes

  1. 1.

    An interesting fact about existence gates is that they are useless in standard electronics, in our scheme they allow a method of recording the presence or absence of a logical signal without knowing anything about the content, which has applications in cryptography, monitoring, meta-data tracking and hacking of such systems.

  2. 2.

    Other than the trivial way of using a high voltage for \(\bigcirc \) and a low voltage for \(|\).

  3. 3.

    \(\{\rightarrow ,\bot \}\),\(\{\leftarrow , \bot \}\), \(\{\not \rightarrow , \top \}\), \(\{\not \leftarrow , \top \}\).

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Author information

Authors and Affiliations

  1. University of Bath, Claverton Down, Somerset, Bath, BA2 7AY, UK

    Ella Gale

  2. International Center for Unconventional Computing, University of the West of England, Coldharbour Lane, Frenchay, Bristol, BS16 1QY, UK

    Ella Gale

Authors
  1. Ella Gale
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Correspondence to Ella Gale .

Editor information

Editors and Affiliations

  1. Manchester Metropolitan University, Manchester, United Kingdom

    Martyn Amos

  2. University of British Columbia, Vancouver, BC, Canada

    ANNE CONDON

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Gale, E. (2016). Analysis of Boolean Logic Gates Logical Complexity for Use with Spiking Memristor Gates. In: Amos, M., CONDON, A. (eds) Unconventional Computation and Natural Computation. UCNC 2016. Lecture Notes in Computer Science(), vol 9726. Springer, Cham. https://doi.org/10.1007/978-3-319-41312-9_9

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  • DOI: https://doi.org/10.1007/978-3-319-41312-9_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-41311-2

  • Online ISBN: 978-3-319-41312-9

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