Semitopology: a topological approach to decentralised collaborative action
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866914230624583680 |
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| author | Gabbay, Murdoch |
| author_facet | Gabbay, Murdoch |
| contents | We introduce semitopology, a generalisation of point-set topology that removes the restriction that intersections of open sets need necessarily be open. The intuition is that points represent participants in a decentralised system, and open sets represent collections of participants that collectively have the authority to collaborate to update their local state; we call this an actionable coalition.
Examples of actionable coalition include: majority stakes in proof-of-stake blockchains; communicating peers in peer-to-peer networks; and even pedestrians working together to not bump into one another in the street. Where actionable coalitions exist, they have in common that: collaborations are local (updating the states of the participants in the coalition, but not immediately those of the whole system); collaborations are voluntary (up to and including breaking rules); participants may be heterogeneous in their computing power or in their goals (not all pedestrians want to go to the same place); participants can choose with whom to collaborate; and they are not assumed subject to permission or synchronisation by a central authority.
We develop a topology-flavoured mathematics that goes some way to explaining how and why these complex decentralised systems can exhibit order, and gives us new ways to understand existing practical implementations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_09287 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Semitopology: a topological approach to decentralised collaborative action Gabbay, Murdoch Logic in Computer Science Distributed, Parallel, and Cluster Computing General Topology Logic 54J99 F.3.2 We introduce semitopology, a generalisation of point-set topology that removes the restriction that intersections of open sets need necessarily be open. The intuition is that points represent participants in a decentralised system, and open sets represent collections of participants that collectively have the authority to collaborate to update their local state; we call this an actionable coalition. Examples of actionable coalition include: majority stakes in proof-of-stake blockchains; communicating peers in peer-to-peer networks; and even pedestrians working together to not bump into one another in the street. Where actionable coalitions exist, they have in common that: collaborations are local (updating the states of the participants in the coalition, but not immediately those of the whole system); collaborations are voluntary (up to and including breaking rules); participants may be heterogeneous in their computing power or in their goals (not all pedestrians want to go to the same place); participants can choose with whom to collaborate; and they are not assumed subject to permission or synchronisation by a central authority. We develop a topology-flavoured mathematics that goes some way to explaining how and why these complex decentralised systems can exhibit order, and gives us new ways to understand existing practical implementations. |
| title | Semitopology: a topological approach to decentralised collaborative action |
| topic | Logic in Computer Science Distributed, Parallel, and Cluster Computing General Topology Logic 54J99 F.3.2 |
| url | https://arxiv.org/abs/2303.09287 |