# Open Problems in a Logic of Gossips

## TL;DR

This paper discusses open problems in a logic for distributed gossip protocols, highlighting unresolved questions about their semantics, correctness, and extensions with common knowledge, despite recent advances in their formal verification.

## Contribution

It identifies and clarifies key open issues in the logic of gossip protocols, providing background and partial results to guide future research.

## Key findings

- Decidability of semantics and truth for the logic
- Decidability of the logic with common knowledge operator
- Identification of open questions and challenges

## Abstract

Gossip protocols are programs used in a setting in which each agent holds a secret and the aim is to reach a situation in which all agents know all secrets. Such protocols rely on a point-to-point or group communication. Distributed epistemic gossip protocols use epistemic formulas in the component programs for the agents. The advantage of the use of epistemic logic is that the resulting protocols are very concise and amenable for a simple verification. Recently, we introduced a natural modal logic that allows one to express distributed epistemic gossip protocols and to reason about their correctness. We proved that the resulting protocols are implementable and that all aspects of their correctness, including termination, are decidable. To establish these results we showed that both the definition of semantics and of truth of the underlying logic are decidable. We also showed that the analogous results hold for an extension of this logic with the 'common knowledge' operator. However, several, often deceptively simple, questions about this logic and the corresponding gossip protocols remain open. The purpose of this paper is to list and elucidate these questions and provide for them an appropriate background information in the form of partial of related results.