Acta Informatica

, Volume 52, Issue 2–3, pp 175–205 | Cite as

CCS: It’s not fair!

Fair schedulers cannot be implemented in CCS-like languages even under progress and certain fairness assumptions
Original Article

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.

Notes

Acknowledgments

We gratefully thank the anonymous referees. Their reports showed deep insights in the material, and helped a lot to improve the quality of the paper. In particular, the link between our fair scheduler and Peterson’s mutual exclusion protocol was made by one of the referees.

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Authors and Affiliations

  1. 1.NICTASydneyAustralia
  2. 2.UNSWSydneyAustralia

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