On the limit cycle structure of threshold boolean networks over complete graphs

In previous work, the limit structure of positive and negative finite threshold boolean networks without inputs (TBNs) over the complete digraph K(n) was analyzed and an algorithm was presented for computing this structure in polynomial time. Those results are generalized in this paper to cover the case of arbitrary TBNs over K(n). Although the limit structure is now more complicated, containing, not only fixed-points and cycles of length 2, but possibly also cycles of arbitrary length, a simple algorithm is still available for its determination in polynomial time. Finally, the algorithm is generalized to cover the case of symmetric finite boolean networks over K(n).