Complexity of fixed point counting problems in Boolean networks

A Boolean network (BN) with n components is a discrete dynamical system described by the successive iterations of function f:{0,1}n?{0,1}n. This model finds applications in biology, where fixed points play central role. For example, genetic regulations, they correspond to cell phenotypes. In this context, experiments reveal existence positive or negative influences among components. The digraph called signed interaction (SID), and one SID may large number BNs. present work opens new perspective on well-established study When biologists discover BN do not know, ask: given that SID, can it having at least/at most k points? Depending input, we prove these problems are P complete for NP, NPNP, NP#P NEXPTIME.