TY - JOUR

T1 - An improved satisfiability algorithm for nested canalyzing functions and its application to determining a singleton attractor of a boolean network

AU - Melkman, Avraham A.

AU - Akutsu, Tatsuya

PY - 2013/12/1

Y1 - 2013/12/1

N2 - 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(2k, 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(2k, 1.325k+m, 2m)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.

AB - 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(2k, 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(2k, 1.325k+m, 2m)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.

KW - Boolean network

KW - SAT

KW - nested canalyzing function.

KW - singleton attractor

UR - http://www.scopus.com/inward/record.url?scp=84888323654&partnerID=8YFLogxK

U2 - 10.1089/cmb.2013.0060

DO - 10.1089/cmb.2013.0060

M3 - Article

AN - SCOPUS:84888323654

VL - 20

SP - 958

EP - 969

JO - Journal of Computational Biology

JF - Journal of Computational Biology

SN - 1066-5277

IS - 12

ER -