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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.