A Behavioral Theory for Distributed Systems with Weak Recovery

TL;DR

This paper introduces a formal calculus for modeling distributed systems with crash failures and weak recovery, providing a behavioral theory to reason about system equivalences and fault-tolerance.

Contribution

It presents a novel calculus inspired by Erlang and distributed π-calculus, along with a behavioral theory and weak bisimilarity for reasoning about failures and recovery.

Findings

Developed a formal calculus for crash failures with weak recovery

Established a behavioral equivalence using labelled transition systems

Provided a compositional proof technique for system equivalence

Abstract

Distributed systems can be subject to various kinds of partial failures, therefore building fault-tolerance or failure mitigation mechanisms for distributed systems remains an important domain of research. In this paper, we present a calculus to formally model distributed systems subject to crash failures with recovery. The recovery model considered in the paper is weak, in the sense that it makes no assumption on the exact state in which a failed node resumes its execution, only its identity has to be distinguishable from past incarnations of itself. Our calculus is inspired in part by the Erlang programming language and in part by the distributed $\pi$-calculus with nodes and link failures (D$\pi$F) introduced by Francalanza and Hennessy. In order to reason about distributed systems with failures and recovery we develop a behavioral theory for our calculus, in the form of a contextual equivalence, and of a fully abstract coinductive characterization of this equivalence by means of a labelled transition system semantics and its associated weak bisimilarity. This result is valuable for it provides a compositional proof technique for proving or disproving contextual equivalence between systems.