Abstract
A gossip protocol is a procedure for sharing secrets in a network. The basic action in a gossip protocol is a telephone call wherein the caller and the callee exchange all the secrets they know. An agent who knows all secrets is an expert. The usual termination condition is that all agents are experts. Instead, we explore some protocols wherein the termination condition is that all agents know that all agents are experts. We call such agents super experts. Additionally, we model that agents who already know that all agents are experts, do not make and do not answer calls. We also model that such protocols are common knowledge among the agents. We investigate conditions under which such gossip protocols terminate, both in the synchronous case, where there is a global clock, and in the asynchronous case, where there is not. We show that a protocol with missed calls can terminate faster than the same protocol without missed calls.
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Acknowledgements
Rasoul Ramezanian and Rahim Ramezanian would like to thank Prof. Ardeshir for his support and encouragement during their Ph.D. research. Hans van Ditmarsch very kindly remembers the fabulous Workshop on Modal Logic and its Application in Computer Science, organized at the University of Tehran in 2016, of which he and Mohammad Ardeshir were co-organizers, and the many interactions over many years involving Rasoul Ramezanian and Rahim Ramezanian, thanks to Mohammad Ardeshir’s encouragement and facilitation. We thank a reviewer of the submission for useful comments.
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Ramezanian, R., Ramezanian, R., van Ditmarsch, H., Gattinger, M. (2021). Everyone Knows that Everyone Knows. In: Mojtahedi, M., Rahman, S., Zarepour, M.S. (eds) Mathematics, Logic, and their Philosophies. Logic, Epistemology, and the Unity of Science, vol 49. Springer, Cham. https://doi.org/10.1007/978-3-030-53654-1_5
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