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A Three-Level Hierarchy of Models for Lattices of Boolean Functions

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Computer Aided Systems Theory – EUROCAST 2017 (EUROCAST 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10672))

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Abstract

The utilization of lattices of Boolean functions for the synthesis of circuits combines the benefits of more freedom for optimization with limited calculations on mark functions. We extend the known two-level hierarchy of lattices of Boolean functions by a third level. This new level increases the possibilities of synthesis approaches (An extended abstract of this paper was published in [4].).

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References

  1. Brayton, R.K., Hachtel, G.D., McMullen, C.T., Sangiovanni-Vincentelli, A.: Logic Minimization Algorithms for VLSI Synthesis. Kluwer Academic Publishers, Dordrecht (1984)

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  2. Posthoff, C., Steinbach, B.: Logic Functions and Equations - Binary Models for Computer Science. Springer, Dordrecht (2004)

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  3. Steinbach, B.: Generalized lattices of Boolean functions utilized for derivative operations. In: Materiały konferencyjne KNWS 2013, Łagów, Poland, https://doi.org/10.13140/2.1.1874.3680, pp. 1–17 (2013)

  4. Steinbach, B., Posthoff, C.: A hierarchy of models for lattices of Boolean functions. In: Quesada-Arencibia, A., Rodriguez, J.C., Moreno-Diaz Jr., R., Moreno-Diaz, R. (eds.) Computer Aided System Theory, Extended Abstracts. 16th International Conference on Computer Aided System Theory, EUROCAST 2017, pp. 213–214. IUCTC Universidad de Las Palmas, Grand Canaries (2017). ISBN 978-84-617-8087-7

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  5. Steinbach, B., Posthoff, C.: Boolean differential calculus - theory and applications. J. Comput. Theor. Nanosci. 7(6), 933–981 (2010)

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  6. Steinbach, B., Posthoff, C.: Derivative operations for lattices of Boolean functions. In: Proceedings Reed-Muller Workshop 2013, Toyama, Japan, pp. 110–119 (2013). https://doi.org/10.13140/2.1.2398.6568

  7. Steinbach, B., Posthoff, Ch.: Boolean Differential Calculus. Morgan & Claypool Publishers, San Rafael (2017). ISBN 9781627059220 (paperback). ISBN 9781627056175 (ebook). https://doi.org/10.2200/S00766ED1V01Y201704DCS052

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Authors and Affiliations

  1. Institute of Computer Science, Freiberg University of Mining and Technology, Bernhard-von-Cotta-Str. 2, 09596, Freiberg, Germany

    Bernd Steinbach

  2. The University of the West Indies, St. Augustine Campus, Saint Augustine, Trinidad and Tobago

    Christian Posthoff

Authors
  1. Bernd Steinbach
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  2. Christian Posthoff
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Corresponding author

Correspondence to Bernd Steinbach .

Editor information

Editors and Affiliations

  1. University of Las Palmas de Gran Canaria, Las Palmas de Gran Canaria, Spain

    Roberto Moreno-Díaz

  2. Johannes Kepler University Linz, Linz, Austria

    Franz Pichler

  3. University of Las Palmas de Gran Canaria, Las Palmas de Gran Canaria, Spain

    Alexis Quesada-Arencibia

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Steinbach, B., Posthoff, C. (2018). A Three-Level Hierarchy of Models for Lattices of Boolean Functions. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2017. EUROCAST 2017. Lecture Notes in Computer Science(), vol 10672. Springer, Cham. https://doi.org/10.1007/978-3-319-74727-9_28

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  • DOI: https://doi.org/10.1007/978-3-319-74727-9_28

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-74726-2

  • Online ISBN: 978-3-319-74727-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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