## Abstract

We consider Boolean networks defined on directed graphs in which the state of every node belongs to the set {0; 1}. We think of a node in state 1 as having 'failed'. The state of every node at the next time instant is a function of the states of those nodes that link to it. Nodes fail according to a set of rules, and once a node fails it stays so forever. We develop a mathematical framework that allows us to find the smallest set of nodes whose failure at time zero causes the eventual failure of all nodes in a desired target set. Our methods are based on modeling network dynamics using Boolean polynomials and exploiting their properties. Rather than propagating the state forward using a nonlinear map, we characterize all possible steady-state configurations as the fixed points of the network's dynamics, and provide a simple algorithm for finding all such 'stable' configurations. We demonstrate the utility of our framework with the help of illustrative examples.

Original language | English (US) |
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Title of host publication | 2016 IEEE 55th Conference on Decision and Control, CDC 2016 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 997-1002 |

Number of pages | 6 |

ISBN (Electronic) | 9781509018376 |

DOIs | |

State | Published - Dec 27 2016 |

Event | 55th IEEE Conference on Decision and Control, CDC 2016 - Las Vegas, United States Duration: Dec 12 2016 → Dec 14 2016 |

### Other

Other | 55th IEEE Conference on Decision and Control, CDC 2016 |
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Country/Territory | United States |

City | Las Vegas |

Period | 12/12/16 → 12/14/16 |

## Keywords

- Boolean networks
- Boolean polynomials
- cascading failures

## ASJC Scopus subject areas

- Artificial Intelligence
- Decision Sciences (miscellaneous)
- Control and Optimization