Epistemic protocols for dynamic gossip

A gossip protocol is a procedure for spreading secrets among a group of agents, using a connection graph. In each call between a pair of connected agents, the two agents share all the secrets they have learnt. In dynamic gossip problems, dynamic connection graphs are enabled by permitting agents to spread as well the telephone numbers of other agents they know. This paper characterizes different distributed epistemic protocols in terms of the (largest) class of graphs where each protocol is successful, i.e. where the protocol necessarily ends up with all agents knowing all secrets

Epistemic Gossip Protocols

In this thesis we study epistemic protocols for gossip. Each agent in the gossip scenario knows a unique piece of information which is called a secret. Agents communicate with each other by means of pairwise telephone calls, and in each call the calling pair of agents exchange all the secrets they currently know. In an epistemic gossip protocol, an agent $a$ can call another agent $b$, not because it is so instructed, but because agent $a$ knows that it satisfies some knowledge-based condition defined by the protocol. The goal of gossiping is typically epistemic, for example, that after a sequence of calls, every agent knows the secret of every other agent. The question then arises as to which knowledge conditions bring about the goal of gossiping, and what properties the resulting protocols have. In this thesis we describe a theoretical framework for the study of epistemic gossip protocols based on dynamic epistemic logic. We describe a number of epistemic gossip protocols and formalise these protocols using our theoretical framework. We study and prove the dynamic properties of these protocols in various types of underlying network topologies such as the line topology network, circle topology network, tree topology network, and the complete topology network. Based on our theoretical framework, we implement a software framework for describing, modelling and checking the dynamic properties of epistemic gossip protocols. We call this software framework the Epistemic Gossip Protocol (EGP) tool. The EGP tool automates the checking of dynamic properties of a given epistemic gossip protocol, such as, whether the given protocol achieves the goal of gossiping for every execution sequence of the protocol, whether the given protocol can produce execution sequences that lead to a deadlock, or whether the given protocol can produce an infinite execution sequence due to a loop. We describe the details of the implementation of the EGP tool, and use the tool to model, and check the dynamic properties of our example protocols. We present and discuss the results obtained from our experiments with the EGP tool

Strengthening Gossip Protocols using Protocol-Dependent Knowledge

Distributed dynamic gossip is a generalization of the classic telephone problem in which agents communicate to share secrets, with the additional twist that also telephone numbers are exchanged to determine who can call whom. Recent work focused on the success conditions of simple protocols such as “Learn New Secrets” (LNS) wherein an agent a may only call another agent b if a does not know b’s secret. A protocol execution is successful if all agents get to know all secrets. On partial networks these protocols sometimes fail because they ignore information available to the agents that would allow for better coordination. We study how epistemic protocols for dynamic gossip can be strengthened, using epistemic logic as a simple protocol language with a new operator for protocol-dependent knowledge. We provide definitions of different strengthenings and show that they perform better than LNS, but we also prove that there is no strengthening of LNS that always terminates successfully. Together, this gives us a better picture of when and how epistemic coordination can help in the dynamic gossip problem in particular and distributed systems in general

New Directions in Model Checking Dynamic Epistemic Logic

Dynamic Epistemic Logic (DEL) can model complex information scenarios in a way that appeals to logicians. However, its existing implementations are based on explicit model checking which can only deal with small models, so we do not know how DEL performs for larger and real-world problems. For temporal logics, in contrast, symbolic model checking has been developed and successfully applied, for example in protocol and hardware verification. Symbolic model checkers for temporal logics are very efficient and can deal with very large models. In this thesis we build a bridge: new faithful representations of DEL models as so-called knowledge and belief structures that allow for symbolic model checking. For complex epistemic and factual change we introduce transformers, a symbolic replacement for action models. Besides a detailed explanation of the theory, we present SMCDEL: a Haskell implementation of symbolic model checking for DEL using Binary Decision Diagrams. Our new methods can solve well-known benchmark problems in epistemic scenarios much faster than existing methods for DEL. We also compare its performance to to existing model checkers for temporal logics and show that DEL can compete with established frameworks. We zoom in on two specific variants of DEL for concrete applications. First, we introduce Public Inspection Logic, a new framework for the knowledge of variables and its dynamics. Second, we study the dynamic gossip problem and how it can be analyzed with epistemic logic. We show that existing gossip protocols can be improved, but that no perfect strengthening of "Learn New Secrets" exists

Everyone Knows that Everyone Knows: Gossip Protocols for Super Experts

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 calling agents 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 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 are super experts do not make and do not answer calls. Such agents are called engaged agents. We also model that such gossip protocols are common knowledge among the agents. We investigate conditions under which 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 commonly known protocol with engaged agents may terminate faster than the same protocol without engaged agents

Everyone Knows that Everyone Knows:Gossip Protocols for Super Experts

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 calling agents 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 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 are super experts do not make and do not answer calls. Such agents are called engaged agents. We also model that such gossip protocols are common knowledge among the agents. We investigate conditions under which 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 commonly known protocol with engaged agents may terminate faster than the same protocol without engaged agents