eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2017-09-01
12:1
12:16
10.4230/LIPIcs.CONCUR.2017.12
article
Controlling a Population
Bertrand, Nathalie
Dewaskar, Miheer
Genest, Blaise
Gimbert, Hugo
We introduce a new setting where a population of agents, each modelled by a finite-state 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 non-deterministic finite state automaton (NFA), the same for every agent, and the whole system is encoded as a 2-player game. The first player chooses actions, and the second player resolves non-determinism for each agent. The game with m agents is called the m-population 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 m-population 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 EXPTIME-complete problem. As far as we know, this is one of the first results on parameterized control. Our algorithm, not based on cut-off 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 m-population 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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol085-concur2017/LIPIcs.CONCUR.2017.12/LIPIcs.CONCUR.2017.12.pdf
Model-checking
control
parametric systems