Population Protocols on Graphs: A Hierarchy

Bournez, Olivier; Lefèvre, Jonas

doi:10.1007/978-3-642-39074-6_5

Cited by 2 publications

(3 citation statements)

References 8 publications

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“…For bounded-degree networks (a well-motivated restriction in a biological setting, also used in e.g. in [3,12]), the picture becomes more complex. Counting and non-counting automata become equally powerful, an interesting fact because biological models are often non-counting.…”

Section: Discussionmentioning

confidence: 99%

Decision Power of Weak Asynchronous Models of Distributed Computing

Czerner

Guttenberg

Helfrich

et al. 2021

Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing

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Esparza and Reiter have recently conducted a systematic comparative study of models of distributed computing consisting of a network of identical finite-state automata that cooperate to decide if the underlying graph of the network satisfies a given property.The study classifies models according to four criteria, and shows that twenty-four initially possible combinations collapse into seven equivalence classes with respect to their decision power, i.e. the properties that the automata of each class can decide. However, Esparza and Reiter only show (proper) inclusions between the classes, and so do not characterise their decision power. In this paper we do so for labelling properties, i.e. properties that depend only on the labels of the nodes, but not on the structure of the graph. In particular, majority (whether more nodes carry label than ) is a labelling property. Our results show that only one of the seven equivalence classes identified by Esparza and Reiter can decide majority for arbitrary networks. We then study the expressive power of the classes on bounded-degree networks, and show that three classes can. In particular, we present an algorithm for majority that works for all bounded-degree networks under adversarial schedulers, i.e. even if the scheduler must only satisfy that every node makes a move infinitely often, and prove that no such algorithm can work for arbitrary networks.

show abstract

Section: Discussionmentioning

confidence: 99%

Decision Power of Weak Asynchronous Models of Distributed Computing

Czerner

Guttenberg

Helfrich

et al. 2021

Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing

View full text Add to dashboard Cite

show abstract

“…For bounded-degree networks (a well-motivated restriction in a biological setting, also used in previous work, e.g. in [3,13]), the picture becomes more complex. Counting and non-counting automata become equally powerful, an interesting fact for non-counting biological models where events are triggered by the concentration of a substance exceeding a threshold.…”

Section: Discussionmentioning

confidence: 99%

“…We start by proving that labelling properties ϕ ∈ NSPACE(n) can be decided. By [13], when restricting to k-degree-bounded graphs, graph population protocols can decide all symmetric properties ϕ ∈ NSPACE(n), in particular all labelling properties ϕ ∈ NSPACE(n), since they are by definition invariant under rearranging the labels. By Lemma 11, all properties decidable by graph population protocols can also be decided by DAF-automata.…”

Section: Lemmamentioning

confidence: 99%

Decision Power of Weak Asynchronous Models of Distributed Computing

Czerner,

Guttenberg,

Helfrich

et al. 2021

Preprint

View full text Add to dashboard Cite

Esparza and Reiter have recently conducted a systematic comparative study of models of distributed computing consisting of a network of identical finite-state automata that cooperate to decide if the underlying graph of the network satisfies a given property. The study classifies models according to four criteria, and shows that twenty initially possible combinations collapse into seven equivalence classes with respect to their decision power, i.e. the properties that the automata of each class can decide. However, Esparza and Reiter only show (proper) inclusions between the classes, and so do not characterise their decision power. In this paper we do so for labelling properties, i.e. properties that depend only on the labels of the nodes, but not on the structure of the graph. In particular, majority (whether more nodes carry label a than b) is a labelling property. Our results show that only one of the seven equivalence classes identified by Esparza and Reiter can decide majority for arbitrary networks. We then study the expressive power of the classes on bounded-degree networks, and show that three classes can. In particular, we present an algorithm for majority that works for all bounded-degree networks under adversarial schedulers, i.e. even if the scheduler must only satisfy that every node makes a move infinitely often, and prove that no such algorithm can work for arbitrary networks.

show abstract

Population Protocols on Graphs: A Hierarchy

Cited by 2 publications

References 8 publications

Decision Power of Weak Asynchronous Models of Distributed Computing

Decision Power of Weak Asynchronous Models of Distributed Computing

Decision Power of Weak Asynchronous Models of Distributed Computing

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