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Minimal Number of Calls in Propositional Protocols

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Reachability Problems (RP 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 13035))

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Abstract

Gossip protocols are programs that can be used by a group of agents to synchronise what information they have. Namely, assuming each agent holds a secret, the goal of a protocol is to reach a situation in which all agents are experts, i.e., know all secrets. Distributed epistemic gossip protocols use epistemic formulas in the component programs for the agents. In this paper, we investigate in-depth one of the simplest classes of such gossip protocols: propositional gossip protocols, in which whether an agent wants to initiate a call depends only the set of secrets that the agent currently knows. We establish important properties about the order of calls possible in a correct propositional gossip protocol, i.e., a one that terminates in the desired all-expert state. This allows us to solve the following open problem: all correct propositional gossip protocols for \(n \ge 4\) agents require at least \(2n-2\) calls in the worst case.

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Authors and Affiliations

  1. University of Liverpool, Liverpool, UK

    Joseph Livesey & Dominik Wojtczak

Authors
  1. Joseph Livesey
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  2. Dominik Wojtczak
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Correspondence to Joseph Livesey or Dominik Wojtczak .

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Editors and Affiliations

  1. Liverpool John Moores University, Liverpool, UK

    Paul C. Bell

  2. University of Liverpool, Liverpool, UK

    Patrick Totzke

  3. University of Liverpool, Liverpool, UK

    Igor Potapov

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Livesey, J., Wojtczak, D. (2021). Minimal Number of Calls in Propositional Protocols. In: Bell, P.C., Totzke, P., Potapov, I. (eds) Reachability Problems. RP 2021. Lecture Notes in Computer Science(), vol 13035. Springer, Cham. https://doi.org/10.1007/978-3-030-89716-1_9

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  • DOI: https://doi.org/10.1007/978-3-030-89716-1_9

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