Title :
A remark on "Scalar equations for synchronous Boolean networks with biological Applications" by C. Farrow, J. Heidel, J. Maloney, and J. Rogers
Author_Institution :
Dept. of Autom., Tsinghua Univ., Beijing, China
Abstract :
The problem of finding all cycles in the exponentially growing state space of synchronous Boolean networks was studied in the paper by C. Farrow, J. Heidel, J. Maloney, and J. R. Scalar, "Equations for synchronous Boolean networks with biological applications," IEEE Trans. Neural Networks, vol. 15, no. 2, pp. 348-354 Mar. 2004. No efficient algorithm was given to solve the problem. We show that even the determination of the number of fixed points (cycles of length 1) for monotone Boolean networks and the determination of the existence of fixed points for general Boolean networks are both strong NP-complete.
Keywords :
Boolean functions; computational complexity; living systems; nonlinear equations; synchronisation; NP-complete; biological application; exponentially growing state space; fixed points; monotone Boolean network; neural network; scalar equation; synchronous Boolean network cycles; Biological information theory; Boolean functions; Computer networks; Encoding; Equations; Neural networks; Power generation; Power systems; Recurrent neural networks; State-space methods; Cycles; fixed points; synchronous Boolean networks; Algorithms; Computer Simulation; Models, Biological; Neural Networks (Computer); Numerical Analysis, Computer-Assisted; Signal Processing, Computer-Assisted;
Journal_Title :
Neural Networks, IEEE Transactions on
DOI :
10.1109/TNN.2005.857944
