Quasi-symmetric logic networks have Lyapunov functions

The authors consider that asynchronous behavior of logic networks which have a certain type of Lyapunov function associated with them. After reviewing the necessary and sufficient conditions for the existence of Lyapunov functions, they analyze the linear case to have a generalized quasi-symmetric condition for component Boolean functions with higher order threshold representation. They also derive explicit forms of Lyapunov functions under this condition. It is shown that generalized quasi-symmetric conditions are sufficient for a logic net to have Lyapunov functions.<<ETX>>

[1]  Martin Hasler,et al.  Recursive neural networks for associative memory , 1990, Wiley-interscience series in systems and optimization.

[2]  Youichi Kobuchi.  State evaluation functions and Lyapunov functions for neural networks , 1991, Neural Networks.

[3]  Pierre Baldi,et al.  Neural networks, orientations of the hypercube, and algebraic threshold functions , 1988, IEEE Trans. Inf. Theory.

[4]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.