CCS: It's not Fair! Fair Schedulers cannot be implemented in CCS-like languages even under progress and certain fairness assumptions

Abstract

In the process algebra community it is sometimes suggested that, on some level of abstraction, any distributed system can be modelled in standard process-algebraic specification formalisms like CCS. This sentiment is strengthened by results testifying that CCS, like many similar formalisms, is Turing powerful and provides a mechanism for interaction. This paper counters that sentiment by presenting a simple fair scheduler---one that in suitable variations occurs in many distributed systems---of which no implementation can be expressed in CCS, unless CCS is enriched with a fairness assumption. Since Dekker's and Peterson's mutual exclusion protocols implement fair schedulers, it follows that these protocols cannot be rendered correctly in CCS without imposing a fairness assumption. Peterson expressed this algorithm correctly in pseudocode without resorting to a fairness assumption, so it furthermore follows that CCS lacks the expressive power to accurately capture such pseudocode.

References in corpus (3)

• A Process Algebra for Wireless Mesh Networks used for Modelling, Verifying and Analysing AODV
• Abstract Processes of Place/Transition Systems
• Progress, Fairness and Justness in Process Algebra

Cited by in corpus (9)

• Progress, Justness and Fairness
• Structure Preserving Bisimilarity, Supporting an Operational Petri Net Semantics of CCSP
• Analysing Mutual Exclusion using Process Algebra with Signals
• Ensuring Liveness Properties of Distributed Systems: Open Problems
• A process algebra with global variables
• Reactive Bisimulation Semantics for a Process Algebra with Time-Outs
• Justness: A Completeness Criterion for Capturing Liveness Properties
• Reactive Temporal Logic
• Modelling Mutual Exclusion in a Process Algebra with Time-outs