CCS: It’s not fair!

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.

Analysing Mutual Exclusion using Process Algebra with Signals

“…The above reasoning merely shows that the given implementation of Peterson's mutual exclusion protocol in CCS requires fairness to be correct. In [20] we show that the same holds for any implementation of any mutual exclusion protocol in CCS, and the same argument applies to a wider class of process algebras. Peterson expressed his protocol in pseudocode without resorting to a fairness assumption.…”

“…In [20] it is shown that Peterson's mutual exclusion protocol [31] cannot be expressed in CCS without assuming fairness. In this section we briefly recapitulate the protocol itself and present an optimal rendering in CCS.…”

“…However, this sentiment has been proven incorrect [20]: two of the authors presented 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. Instances of our fair scheduler, that hence cannot be rendered correctly, are the First in First out 1 , Round Robin, and Fair Queueing scheduling algorithms 2 as used in network routers [28,29] and operating systems [23], or the Completely Fair Scheduler 3 , which is the default scheduler of the Linux kernel since version 2.6.23.…”

Progress, Justness, and Fairness

“…In [18,27] we argue that a justness assumption is essential for the validity of any mutual exclusion protocol. It appears that in the correctness arguments of famous mutual exclusion protocols appearing in the literature [35,49] the relevant justness assumption is taken for granted, without explicit acknowledgement that the correctness of the protocol rests on the validity of this assumption.…”

“…In CCS, the only non-blocking action is τ . However, for certain applications it makes sense to declare some other actions to be non-blocking [27]; this constitutes a promise that we will never put the system in an environment that can block these actions. In [28] we use a process algebra with broadcast communication: a broadcast counts as a non-blocking action, because it will happen regardless whether anyone receives it.…”