Ensuring Liveness Properties of Distributed Systems: Open Problems

TL;DR

This paper proposes a research agenda to develop a new theoretical framework for verifying liveness properties in distributed systems without relying on fairness assumptions, addressing limitations of current models.

Contribution

It introduces a foundational approach combining process algebra, temporal logic, and semantic models to accurately specify and verify distributed systems' liveness without fairness assumptions.

Findings

Current models fail to distinguish systems with crucial liveness properties without fairness.

A new framework requires novel induction principles and axiomatic bases.

Standard process algebras cannot specify simple systems like fair schedulers without fairness.

Abstract

Often fairness assumptions need to be made in order to establish liveness properties of distributed systems, but in many situations they lead to false conclusions. This document presents a research agenda aiming at laying the foundations of a theory of concurrency that is equipped to ensure liveness properties of distributed systems without making fairness assumptions. This theory will encompass process algebra, temporal logic and semantic models. The agenda also includes the development of a methodology and tools that allow successful application of this theory to the specification, analysis and verification of realistic distributed systems. Contemporary process algebras and temporal logics fail to make distinctions between systems of which one has a crucial liveness property and the other does not, at least when assuming justness, a strong progress property, but not assuming fairness. Setting up an alternative framework involves giving up on identifying strongly bisimilar systems, inventing new induction principles, developing new axiomatic bases for process algebras and new congruence formats for operational semantics, and creating matching treatments of time and probability. Even simple systems like fair schedulers or mutual exclusion protocols cannot be accurately specified in standard process algebras (or Petri nets) in the absence of fairness assumptions. Hence the work involves the study of adequate language or model extensions, and their expressive power.