### Abstract

We consider in the following the problem of realizing periodic functions by a collection of finite state-agents that cooperate by interacting with each other. More formally, given a periodic non-negative integer function f that maps the set of non-negative integers N to itself, we aim in this paper at designing a distributed protocol with a state set Q and a subset S ⊆ Q, such that, for any initial configuration C_{0}, with probability 1, there are a time instant t_{0} and a constant d ∈ N satisfying f(t + d) = ν_{S}(Ct) for all t ≥ t_{0}, where ν_{S}(C) is the number of agents with a state in S in a configuration C. The model that we consider is a variant of the population protocol (PP) model in which we assume that each agent is involved in an interaction at each time instant t, hence the notion of synchronous handshakes. These additional assumptions on the model are necessary to solve the considered problem. We also assume that the interacting pairs are matched uniformly at random.

Original language | English |
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Title of host publication | Theory and Practice of Natural Computing - 5th International Conference, TPNC 2016, Proceedings |

Editors | Miguel A. Vega-Rodríguez, Carlos Martín-Vide, Takaaki Mizuki |

Publisher | Springer Verlag |

Pages | 21-33 |

Number of pages | 13 |

ISBN (Print) | 9783319490007 |

DOIs | |

Publication status | Published - Jan 1 2016 |

Event | 5th International Conference on Theory and Practice of Natural Computing, TPNC 2016 - Sendai, Japan Duration: Dec 12 2016 → Dec 13 2016 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 10071 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 5th International Conference on Theory and Practice of Natural Computing, TPNC 2016 |
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Country | Japan |

City | Sendai |

Period | 12/12/16 → 12/13/16 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Theory and Practice of Natural Computing - 5th International Conference, TPNC 2016, Proceedings*(pp. 21-33). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10071 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-49001-4_2