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

  • Bernd SteinbachEmail author
  • Christian Posthoff
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10672)

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].).

Keywords

Lattice Boolean function Hierarchy Mark function Derivative operation Independence function Independence matrix Rank 

References

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    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 978-84-617-8087-7Google Scholar
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    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
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    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

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Institute of Computer ScienceFreiberg University of Mining and TechnologyFreibergGermany
  2. 2.The University of the West IndiesSt. Augustine CampusSaint AugustineTrinidad and Tobago

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