An improved satisfiability algorithm for nested canalyzing functions and its application to determining a singleton attractor of a boolean network

We study the problem of finding a 0-1 assignment to Boolean variables satisfying a given set of nested canalyzing functions, a class of Boolean functions that is known to be of interest in biology. For this problem, an extension of the satisfiability problem for a conjunctive normal form formula, an O(min(2^k, 2^(k+m)/2)poly(m)) time algorithm has been known, where m and k are the number of nested canalyzing functions and variables, respectively. Here we present an improved O(min(2^k, 1.325^k+m, 2^m)poly(m)) time algorithm for this problem. We also study the problem of finding a singleton attractor of a Boolean network consisting of n nested canalyzing functions. Although an O(1.799ⁿ) time algorithm was proposed in a previous study, it was implicitly assumed that the network does not contain any positive self-loops. By utilizing the improved satisfiability algorithm for nested canalyzing functions, while allowing for the presence of positive self-loops, we show that the general case can be solved in O(1.871ⁿ) time.