Abstract
In this paper We study some measures of complexity for Boolean functions based on Abstract Harmonic Analysis. More precisely, we extend the notion of average sensitivity of Boolean functions and introduce the generalized sensitivity (or k-sensitivity) which accounts for the changes in the function value when k input bits are flipped. We find the connection between k-sensitivity and Fourier coefficients. We then analyze some properties of the 2-sensitivity and in particular its relation with the average sensitivity (or 1-sensitivity).
This work has been partly supported by the Italian National Research Council, under the “Progetto Finalizzato Sistemi Informatici e Calcolo Parallelo”, subproject 2 “Processori dedicati”.
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© 1994 Springer-Verlag Berlin Heidelberg
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Bernasconi, A., Codenotti, B. (1994). Measures of Boolean function complexity based on Harmonic Analysis. In: Bonuccelli, M., Crescenzi, P., Petreschi, R. (eds) Algorithms and Complexity. CIAC 1994. Lecture Notes in Computer Science, vol 778. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57811-0_7
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DOI: https://doi.org/10.1007/3-540-57811-0_7
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