3 research outputs found
Complexity of fixed point counting problems in Boolean Networks
A Boolean network (BN) with components is a discrete dynamical system
described by the successive iterations of a function . This model finds applications in biology, where fixed points play a
central role. For example, in genetic regulations, they correspond to cell
phenotypes. In this context, experiments reveal the existence of positive or
negative influences among components: component has a positive (resp.
negative) influence on component meaning that tends to mimic (resp.
negate) . The digraph of influences is called signed interaction digraph
(SID), and one SID may correspond to a large number of BNs (which is, in
average, doubly exponential according to ). The present work opens a new
perspective on the well-established study of fixed points in BNs. When
biologists discover the SID of a BN they do not know, they may ask: given that
SID, can it correspond to a BN having at least/at most fixed points?
Depending on the input, we prove that these problems are in or
complete for , ,
\textrm{NP}^{\textrm{#P}} or . In particular, we prove
that it is -complete (resp. -complete) to
decide if a given SID can correspond to a BN having at least two fixed points
(resp. no fixed point).Comment: 43 page