Abstract
This paper investigates the monostability and bistability of Boolean networks using semitensor products (STPs). A theorem characterizing the stability of a Boolean network is presented and then used to develop three new algorithms. The first determines the stability in $O(2^n)$ , a marked improvement of the complexity of $O((2^n-1)2^{2.81n})$ , the results from simply using Strassen's recursive algorithm. The second algorithm computes the transient period of a given system state, and the last one maximizes this over an entire Boolean network. We conclude by applying these algorithms to two published Boolean models of well-known biological networks in E. coli .
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