2023/03/16 by Murdoch J. Gabbay, Gabbay, Murdoch · 1 citation
Computer Science · Decision Sciences · #54J99 #Distributed #F.3.2 #FOS: Computer and information sciences #FOS: Mathematics #Game Theory and Applications #General Topology (math.GN) #Logic (math.LO) #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Parallel #Peer-to-Peer Network Technologies #and Cluster Computing (cs.DC)
paper · pdf · doi:10.48550/arxiv.2303.09287
openalex publication_date 2023/03/16 · openalex created_date 2023/03/19 · openalex updated_date 2026/07/28
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.