Compositional complexity of Boolean functions

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 ...

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...

The complexity of Boolean functions

Sensitivity Versus Certificate Complexity of Boolean Functions

Sensitivity, block sensitivity and certificate complexity are basic complexity measures of Boolean functions. The famous sensitivity conjecture claims that sensitivity is polynomially related to block sensitivity. However, it has been notoriously hard to obtain even exponential bounds. Since block sensitivity is known to be polynomially related to certificate complexity, an equivalent of provin...

Complexity Measures of Cryptographically Secure Boolean Functions

In stream cipher cryptography a pseudorandom sequence of bits of length equal to the message length is generated. This sequence is then bitwise XORed (addition modulo 2) with the message sequence and the resulting sequence is transmitted. At the receiving end, deciphering is done by generating the same pseudorandom sequence and bitwise XORing the cipher bits with the random bits. The seed of th...