## Abstract

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(1.799^{n}) 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(1.871^{n}) time.

Original language | English |
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Pages (from-to) | 958-969 |

Number of pages | 12 |

Journal | Journal of Computational Biology |

Volume | 20 |

Issue number | 12 |

DOIs | |

State | Published - 1 Dec 2013 |

## Keywords

- Boolean network
- SAT
- nested canalyzing function.
- singleton attractor

## ASJC Scopus subject areas

- Modeling and Simulation
- Molecular Biology
- Genetics
- Computational Mathematics
- Computational Theory and Mathematics