Classes of boolean functions with limited complexity

Nonuniform Hard Boolean Functions and Uniform Complexity Classes

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

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 ...

Boolean complexity classes vs. their arithmetic analogs

This paper provides logspace and small circuit depth analogs of the result of Valiant and Vazirani, which is a randomized (or nonuniform) reduction from NP to its arithmetic analog ⊕P . We show a similar randomized reduction between the Boolean classes NL and semiunbounded fan-in Boolean circuits and their arithmetic counterparts. These reductions are based on the Isolation Lemma of Mulmuley, V...