A Behavioral Theory for Distributed Systems with Weak Recovery

2024-06-18

arXiv.org

AI Summary

This paper addresses the challenge of rigorously verifying reliability in distributed systems subject to crash failures and weak recovery—where node identities remain distinguishable but no assumptions are made about initial recovery states. Methodologically, we propose the first fully abstract coinductive behavioral equivalence theory for such settings. We design a process model integrating Erlang semantics with the distributed π-calculus (DπF), explicitly supporting node failure and identity-aware recovery. We define a weak bisimulation semantics over a labeled transition system and prove its full abstraction with respect to contextual equivalence. Our contribution fills a foundational gap in formal equivalence theory for fault-tolerant systems under weak recovery, providing the first compositional and proof-carrying framework for behavioral equivalence of failure-recovery systems. This significantly enhances both the precision and practical applicability of reliability analysis for distributed protocols.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Knowledge Representation and Reasoning: Diagnosis and Abductive Reasoning

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Federated Web and WoT systems, including distributed, federated and edge-based data processing
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

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.

Problem

• Distributed Systems
• Fault Tolerance
• Functional Equivalence

Innovation

• Distributed System Recovery
• System Function Equivalence
• Erlang Programming