# Playing With Population Protocols

@inproceedings{Bournez2008PlayingWP, title={Playing With Population Protocols}, author={Olivier Bournez and J{\'e}r{\'e}mie Chalopin and Johanne Cohen and Xavier Koegler}, booktitle={CSP}, year={2008} }

Population protocols have been introduced as a model of sensor networks consisting of very limited mobile agents with no control over their own movement: A collection of anonymous agents, modeled by finite automata, interact in pairs according to some rules.
Predicates on the initial configurations that can be computed by such protocols have been characterized under several hypotheses.
We discuss here whether and when the rules of interactions between agents can be seen as a game from game…

## 15 Citations

### Computing with Pavlovian Populations

- Computer ScienceOPODIS
- 2011

This work investigates under which conditions population protocols, or more generally pairwise interaction rules, correspond to games and shows that restricting to asymetric games is not really a restriction: all predicates computable by protocols can actually be computed by protocols corresponding to games, i.e. any semi-linear predicate can be compute by a Pavlovian population multi-protocol.

### Asymetric Pavlovian Populations

- Computer ScienceArXiv
- 2011

This work investigates under which conditions population protocols, or more generally pairwise interaction rules, correspond to games and shows that restricting to asymetric games is not really a restric- tion: all predicates computable by protocols can actually be computed by protocols corresponding to games, i.e. any semi-linear predicate can be compute by a Pavlovian population multi-protocol.

### Time-Optimal Self-Stabilizing Leader Election in Population Protocols

- Computer Science, MathematicsPODC
- 2021

This work introduces a silent protocol that uses optimal O(n) parallel time and states and shows that it is possible to solve self-stabilizing leader election in asymptotically optimal expected parallel time of O(log n), but using at least exponential states (a quasi-polynomial number of bits).

### Mediated Population Protocols

- Mathematics, Computer ScienceICALP
- 2009

The mediated protocols are stronger than the classical population protocols, by presenting a MPP for a non-semilinear predicate and a general theorem about the composition of two stably computing mediated population protocols is proved.

### Brief Announcement: Space-Optimal Naming in Population Protocols

- Computer SciencePODC
- 2018

This paper gives a brief presentation of a comprehensive study on the necessary and sufficient state space conditions for the deterministic naming task in the population protocol model. This problem…

### Space-Optimal Counting in Population Protocols

- Computer Science, MathematicsDISC
- 2015

This work significantly improves the previous results known for counting in this model, in terms of exact space complexity, and presents and proves correct the first space-optimal protocols solving the problem for two classical types of fairness, global and weak.

### Computational models for networks of tiny artifacts: A survey

- Computer ScienceComput. Sci. Rev.
- 2011

### Space-Optimal Counting in Population Protocols [Extended Version]

- Computer Science, Mathematics
- 2015

This work significantly improves the previous results known for counting in this distributed communication model of population protocols of finite state, anonymous and asynchronous mobile devices communicating in pairs, in terms of (exact) space complexity.

### Passively mobile communicating machines that use restricted space

- Computer ScienceFOMC '11
- 2011

A new theoretical model for passively mobile Wireless Sensor Networks, called PM, standing forPassively mobile Machines, is proposed, and it is established that the minimal space requirement for the computation of non-semilinear predicates is <i*O</i>(log log <i>n</i>).

### Passively Mobile Communicating Logarithmic Space Machines

- Computer ScienceArXiv
- 2010

It turns out that the PALOMA model can assign unique consecutive ids to the agents and inform them of the population size, which allows us to give a direct simulation of a Deterministic Turing Machine of O(nlogn) space, thus, establishing that any symmetric predicate in SPACE(NLogn) also belongs to PLM.

## References

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This chapter surveys results that describe what can be computed in various versions of the population protocol model, which can be used to model mobile ad hoc networks of tiny devices or collections of molecules undergoing chemical reactions.

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The computational power of networks of small resource-limited mobile agents is explored. Two new models of computation based on pairwise interactions of finite-state agents in populations of finite…

### Stably computable predicates are semilinear

- Mathematics, Computer SciencePODC '06
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It is proved that all predicates stably computable in this model of population protocols (and certain generalizations of it) are semilinear, answering a central open question about the power of the model.

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This paper takes a first step in that direction by studying an artificial community of agents that uses a notion of trust to succeed in a game against nature, simple enough to analyze and simulate, but also rich enough to exhibit phenomena of real-life interactive communities.

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A stochastic process based on the iterated prisoner's dilemma game, where each player has a state, and the states of the players connected by the edge are modified according to the Pavlov strategy, which converges to a unique absorbing state in which all players cooperate.

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A model is developed based on the concept of an evolutionarily stable strategy in the context of the Prisoner's Dilemma game to show how cooperation based on reciprocity can get started in an asocial world, can thrive while interacting with a wide range of other strategies, and can resist invasion once fully established.

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This text introduces current evolutionary game theory--where ideas from evolutionary biology and rationalistic economics meet--emphasizing the links between static and dynamic approaches and…

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Extended evolutionary simulations of heterogeneous ensembles of probabilistic strategies including mutation and selection are presented and the unexpected success of another protagonist: Pavlov is reported, suggesting that cooperative behaviour in natural situations may often be based on win-stay, lose-shift.

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The behavior of an extended play Prisoner's Dilemma with Pavlov against various opponents is analyzed and it is found that Pavlov and his clone would learn to cooperate more rapidly than if Pavlov played against the Tit for Tat strategy.

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A method, based on the notion of coupling, which makes use of a “horizontal” distance, such thatelta decreases in expectation at each step of a randomized self-stabilizing algorithm, which allows us to assess the convergence rate according to two different measures.