Conjugate symmetry |
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Authors: | Peter M Maurer |
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Affiliation: | (1) Oncology Imaging and Radiotherapy Physics Queen’s Centre for Oncology, Castle Hill Hospital, Cottingham, UK |
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Abstract: | Conjugate symmetry is an entirely new approach to symmetric Boolean functions that can be used to extend existing methods
for handling symmetric functions to a much wider class of functions. These are functions that currently appear to have no
symmetries of any kind. Conjugate symmetries occur widely in practice. In fact, we show that even the simplest circuits exhibit
conjugate symmetry. To demonstrate the effectiveness of conjugate symmetry we modify an existing simulation algorithm, the
hyperlinear algorithm, to take advantage of conjugate symmetry. This algorithm can simulate symmetric functions faster than
non-symmetric ones, but due to the rarity of symmetric functions, this optimization is of limited benefit. Because the standard
benchmark circuits contain many symmetries it is possible to simulate these circuits faster than is possible with the fastest
known event-driven algorithm. The detection and exploitation of conjugate symmetries makes use of GF(2) matrices. It is likely that conjugate symmetry and GF(2) matrices will find applications in many other areas of EDA. |
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