Determining a singleton attractor of a Boolean network with nested canalyzing functions

In this article, we study the problem of finding a singleton attractor for several biologically important subclasses of Boolean networks (BNs). The problem of finding a singleton attractor in a BN is known to be NP-hard in general. For BNs consisting of n nested canalyzing functions, we present an O(1.799 ⁿ) time algorithm. The core part of this development is an O(min(2 ^k/2•2 ^m/2, 2 ^k)•poly(k, m)) time algorithm for the satisfiability problem for m nested canalyzing functions over k variables. For BNs consisting of chain functions, a subclass of nested canalyzing functions, we present an O(1.619 ⁿ) time algorithm and show that the problem remains NP-hard, even though the satisfiability problem for m chain functions over k variables is solvable in polynomial time. Finally, we present an o(2 ⁿ) time algorithm for bounded degree BNs consisting of canalyzing functions.