Abstract
We introduce a new setting where a population of agents, each modelled by a finitestate system, are controlled uniformly: the controller applies the same action to every agent. The framework is largely inspired by the control of a biological system, namely a population of yeasts, where the controller may only change the environment common to all cells. We study a synchronisation problem for such populations: no matter how individual agents react to the actions of the controller, the controller aims at driving all agents synchronously to a target state. The agents are naturally represented by a nondeterministic finite state automaton (NFA), the same for every agent, and the whole system is encoded as a 2player game. The first player chooses actions, and the second player resolves nondeterminism for each agent. The game with m agents is called the mpopulation game. This gives rise to a parameterized control problem (where control refers to 2 player games), namely the population control problem: can playerone control the mpopulation game for all m in N whatever playertwo does?
In this paper, we prove that the population control problem is decidable, and it is a EXPTIMEcomplete problem. As far as we know, this is one of the first results on parameterized control. Our algorithm, not based on cutoff techniques, produces winning strategies which are symbolic, that i they do not need to count precisely how the population is spread between states. We also show that if the is no winning strategy, then there is a population size cutoff such that playerone wins the mpopulation game if and only if m< \cutoff. Surprisingly, \cutoff can be doubly exponential in the number of states of the NFA, with tight upper and lower bounds.
BibTeX  Entry
@InProceedings{bertrand_et_al:LIPIcs:2017:7800,
author = {Nathalie Bertrand and Miheer Dewaskar and Blaise Genest and Hugo Gimbert},
title = {{Controlling a Population}},
booktitle = {28th International Conference on Concurrency Theory (CONCUR 2017)},
pages = {12:112:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959770484},
ISSN = {18688969},
year = {2017},
volume = {85},
editor = {Roland Meyer and Uwe Nestmann},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2017/7800},
URN = {urn:nbn:de:0030drops78000},
doi = {10.4230/LIPIcs.CONCUR.2017.12},
annote = {Keywords: Modelchecking, control, parametric systems}
}
Keywords: 

Modelchecking, control, parametric systems 
Collection: 

28th International Conference on Concurrency Theory (CONCUR 2017) 
Issue Date: 

2017 
Date of publication: 

01.09.2017 