Epistemic Protocols for Distributed Gossiping

Gossip protocols aim at arriving, by means of point-to-point or group communications, at a situation in which all the agents know each other's secrets. We consider distributed gossip protocols which are expressed by means of epistemic logic. We provide an operational semantics of such protocols and set up an appropriate framework to argue about their correctness. Then we analyze specific protocols for complete graphs and for directed rings.Comment: In Proceedings TARK 2015, arXiv:1606.0729

On Decidability of a Logic of Gossips

Gossip protocols aim at arriving, by means of point-to-point or group communications, at a situation in which all the agents know each other secrets, see, e.g., [11]. In [1], building upon [3], we studied distributed epistemic gossip protocols, which are examples of knowledge based prog

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

Verification of distributed epistemic gossip protocols

Gossip protocols aim at arriving, by means of point-to-point or group communications, at a situation in which all the agents know each other secrets. Distributed epistemic gossip protocols use as guards formulas from a simple epistemic logic and as statements calls between the agents. They are natural examples of knowledge based programs.We prove here that these protocols are implementable, that their partial correctness is decidable and that termination and two forms of fair termination of these protocols are decidable, as well. To establish these results we show that the definition of semantics and of truth of the underlying logic are decidable.</p

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

Common Knowledge in a Logic of Gossips

Gossip protocols aim at arriving, by means of point-to-point or group communications, at a situation in which all the agents know each other secrets. Recently a number of authors studied distributed epistemic gossip protocols. These protocols use as guards formulas from a simple epistemic logic, which makes their analysis and verification substantially easier. We study here common knowledge in the context of such a logic. First, we analyze when it can be reduced to iterated knowledge. Then we show that the semantics and truth for formulas without nested common knowledge operator are decidable. This implies that implementability, partial correctness and termination of distributed epistemic gossip protocols that use non-nested common knowledge operator is decidable, as well. Given that common knowledge is equivalent to an infinite conjunction of nested knowledge, these results are non-trivial generalizations of the corresponding decidability results for the original epistemic logic, established in (Apt & Wojtczak, 2016). K. R. Apt & D. Wojtczak (2016): On Decidability of a Logic of Gossips. In Proc. of JELIA 2016, pp. 18-33, doi:10.1007/ 978-3-319-48758-8_2.Comment: In Proceedings TARK 2017, arXiv:1707.0825

Verification of Distributed Epistemic Gossip Protocols

Gossip protocols aim at arriving, by means of point-to-point or group communications, at a situation in which all the agents know each other secrets. Distributed epistemic gossip protocols use as guards formulas from a simple epistemic logic and as statements calls between the agents. They are natural examples of knowledge based programs. We prove here that these protocols are implementable, that their partial correctness is decidable and that termination and two forms of fair termination of these protocols are decidable, as well. To establish these results we show that the definition of semantics and of truth of the underlying logic are decidable

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

When Are Two Gossips the Same? Types of Communication in Epistemic Gossip Protocols

We provide an in-depth study of the knowledge-theoretic aspects of communication in so-called gossip protocols. Pairs of agents communicate by means of calls in order to spread information---so-called secrets---within the group. Depending on the nature of such calls knowledge spreads in different ways within the group. Systematizing existing literature, we identify 18 different types of communication, and model their epistemic effects through corresponding indistinguishability relations. We then provide a classification of these relations and show its usefulness for an epistemic analysis in presence of different communication types. Finally, we explain how to formalise the assumption that the agents have common knowledge of a distributed epistemic gossip protocol