Sperner type theorems and complexity of minimal disjunctive normal forms of monotone boolean functions

1981 ◽  
Vol 12 (4) ◽  
pp. 267-282 ◽  
Author(s):  
H. -D. O. F. Gronau
Keyword(s):  
Boolean Functions ◽  
Normal Forms ◽  
Monotone Boolean Functions

scholarly journals On the Lyapunov Exponent of Monotone Boolean Networks †

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 1035
Author(s):  
Ilya Shmulevich
Keyword(s):  
Lyapunov Exponent ◽  
Dynamical Systems ◽  
Boolean Functions ◽  
Boolean Network ◽  
Discrete Dynamical Systems ◽  
Boolean Networks ◽  
Asymptotic Formulas ◽  
Small Perturbations ◽  
Monotone Boolean Functions ◽  
Almost All

Boolean networks are discrete dynamical systems comprised of coupled Boolean functions. An important parameter that characterizes such systems is the Lyapunov exponent, which measures the state stability of the system to small perturbations. We consider networks comprised of monotone Boolean functions and derive asymptotic formulas for the Lyapunov exponent of almost all monotone Boolean networks. The formulas are different depending on whether the number of variables of the constituent Boolean functions, or equivalently, the connectivity of the Boolean network, is even or odd.

scholarly journals Counting inequivalent monotone Boolean functions

2014 ◽  
Vol 167 ◽  
pp. 15-24 ◽  
Author(s):  
Tamon Stephen ◽  
Timothy Yusun
Keyword(s):  
Boolean Functions ◽  
Monotone Boolean Functions
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