### Abstract

We consider the population protocol (PP) model used to represent a collection of finite-state mobile agents that interact with each other to accomplish a common task. Motivated by the well-known BZ reaction, we address the problem of autonomously generating an oscillatory execution from any initial configuration (i.e., in a self-stabilizing manner). For deterministic PPs under a deterministic scheduler, we show that the self-stabilizing leader election (SS-LE) problem and the self-stabilizing oscillation (SS-OS) problem are equivalent, in the sense that an SS-OS protocol is constructible from a given SS-LE protocol, and vice versa, which unfortunately implies that (1) resorting to a leader is inevitable (although we seek a decentralized solution), (2) n states are necessary to create oscillations of amplitude n, where n is the number of agents (although we seek a memory-efficient solution). Aiming at reducing the space complexity, we present some deterministic oscillatory PPs under a uniform random scheduler.

Original language | English |
---|---|

Pages (from-to) | 336-351 |

Number of pages | 16 |

Journal | Information and Computation |

Volume | 255 |

DOIs | |

Publication status | Published - Aug 2017 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Information Systems
- Computer Science Applications
- Computational Theory and Mathematics

### Cite this

*Information and Computation*,

*255*, 336-351. https://doi.org/10.1016/j.ic.2016.12.002