Detecting a Singleton Attractor in a Boolean Network Utilizing SAT Algorithms

摘要

The Boolean network (BN) is a mathematical model of genetic networks. It is known that detecting a singleton attractor, which is also called a fixed point, is NP-hard even for AND/OR BNs (i.e., BNs consisting of AND/OR nodes), where singleton attractors correspond to steady states. Though a naive algorithm can detect a singleton attractor for an AND/OR BN in O(n2~n) time, no O((2 - ∈)~n) (∈ > 0) time algorithm was known even for an AND/OR BN with non-restricted indegree, where n is the number of nodes in a BN. In this paper, we present an O(1 .787~n) time algorithm for detecting a singleton attractor of a given AND/OR BN, along with related results. We also show that detection of a singleton attractor in a BN with maximum indegree two is NP-hard and can be polynomially reduced to a satisfiability problem.