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Influence of a Set of Variables on a Boolean Function. (arXiv:2107.08676v2 [cs.IT] UPDATED)
June 16, 2022, 1:20 a.m. | Aniruddha Biswas, Palash Sarkar
cs.CR updates on arXiv.org arxiv.org
The influence of a variable is an important concept in the analysis of
Boolean functions. The more general notion of influence of a set of variables
on a Boolean function has four separate definitions in the literature. In the
present work, we introduce a new definition of influence of a set of variables
which is based on the auto-correlation function and develop its basic theory.
Among the new results that we obtain are generalisations of the Poincar\'{e}
inequality and the …
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