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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Balanced Boolean Functions with Good Autocorrelation Spectra and Their Applications
自相关谱 平衡 布尔函数
2023/4/26
In this talk we consider the maximum absolute value in the autocorrelation spectrum (not considering the zero point) of balanced Boolean function. The long-standing open question in this area is to ob...
Locally monotone Boolean and pseudo-Boolean functions
Boolean function pseudo-Boolean function local monotonicity discrete partial derivative join and meet derivatives
2011/9/29
Abstract: We propose local versions of monotonicity for Boolean and pseudo-Boolean functions: say that a pseudo-Boolean (Boolean) function is p-locally monotone if each of its partial derivatives keep...
Sharp Thresholds for Monotone Non Boolean Functions and Social Choice Theory
Non Boolean Functions Social Choice Theory
2010/11/22
A key fact in the theory of Boolean functions $f : \{0,1\}^n \to \{0,1\}$ is that they often undergo sharp thresholds. For example: if the function $f : \{0,1\}^n \to \{0,1\}$ is monotone and symmetr...
On the parity complexity measures of Boolean functions
Computational complexity Communication complexity Parity decision tree Log-Rank conjecture
2012/11/30
The parity decision tree model extends the decision tree model by allowing the computation of a parity function in one step. We prove that the deterministic parity decision tree complexity of any Bool...
We will give the definition of the linear kernel of boolean functions and prove that, by a reversible linear transformation, any linear structure boolean function can be transformed into a boolean fun...
Discrete Dynamical Systems on Graphs and Boolean Functions
Parallel dynamical system (PDS) sequential dynamical system (SDS) Garden of Eden (GOE) state space fixed point periodic point
2014/6/3
Discrete dynamical systems based on dependency graphs have played an important role in the mathematical theory of computer simulations. In this paper, we are concerned with parallel dynamical systems ...