Abstract : We present the properties of a new class of Boolean functions defined as the sum of m symmetric functions with decreasing number of variables and degrees. The choice of this construction is justified by the possibility to study these functions by using tools existing for symmetric functions. On the one hand we show that the synthesis is well understood and give an upper bound on the gate complexity. On the other hand, we investigate the Walsh spectrum of the sum of two functions and get explicit formulae for the case of degree at most three.
https://hal.inria.fr/inria-00338085
Contributor : Marion Videau
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Submitted on : Monday, November 10, 2008 - 5:16:35 PM
Last modification on : Thursday, January 11, 2018 - 6:21:04 AM
Long-term archiving on : Monday, June 7, 2010 - 10:51:44 PM
Cédric Lauradoux, Marion Videau. Matriochka symmetric Boolean functions. IEEE International Symposium on Information Theory - ISIT 2008, Jul 2008, Toronto, Canada. pp.1631-1635, ⟨10.1109/ISIT.2008.4595264⟩. ⟨inria-00338085⟩
