The conjunctive complexity of quadratic Boolean functions

The complexity of Boolean functions

Complexity of Boolean Functions

s of Presentation: Paul Beame: Time-Space Tradeoffs and Multiparty Communication Complexity 9 Beate Bollig: Exponential Lower Bounds for Integer Multiplication Using Universal Hashing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Philipp Wölfel: On k-wise l-mixed Boolean Functions . . . . . . . . . . . . . . 10 Elizabeta Okol’nishnikova: On One Lower Bound for Branching Progra...

Compositional complexity of Boolean functions

We define two measures, y and c, of complexity for Boolean functions. These measures are related to issues of functional decomposition which (for continuous functions) were studied by Arnol’d, Kolmogorov, VituSkin and others in connection with Hilbert’s 13th Problem. ‘This perspective was first applied to Boolean functions in (11. Our complexity measures differ from those which were considered ...

Best Quadratic Approximations of Cubic Boolean Functions

The problem of computing best low order approximations of Boolean functions is treated in this paper. We focus on the case of best quadratic approximations of a wide class of cubic functions of arbitrary number of variables, and provide formulas for their efficient calculation. Our methodology is developed upon Shannon’s expansion formula and properties of best affine approximations of quadrati...

Local Maxima of Quadratic Boolean Functions

Combinatorics, Probability and Computing / Volume 25 / Issue 04 / July 2016, pp 633 640 DOI: 10.1017/S0963548315000322, Published online: 21 December 2015 Link to this article: http://journals.cambridge.org/abstract_S0963548315000322 How to cite this article: HUNTER SPINK (2016). Local Maxima of Quadratic Boolean Functions. Combinatorics, Probability and Computing, 25, pp 633-640 doi:10.1017/S0...