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Fair testing
 Concur ’95: Concurrency Theory, volume 962 of Lecture Notes in Computer Science
, 1995
"... In this paper we present a solution to the longstanding problem of characterising the coarsest livenesspreserving precongruence with respect to a full (TCSPinspired) process algebra. In fact, we present two distinct characterisations, which give rise to the same relation: an operational one base ..."
Abstract

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In this paper we present a solution to the longstanding problem of characterising the coarsest livenesspreserving precongruence with respect to a full (TCSPinspired) process algebra. In fact, we present two distinct characterisations, which give rise to the same relation: an operational one based on a De NicolaHennessylike testing modality which we call shouldtesting, and a denotational one based on a refined notion of failures. One of the distinguishing characteristics of the shouldtesting precongruence is that it abstracts from divergences in the same way as Milner’s observation congruence, and as a consequence is strictly coarser than observation congruence. In other words, shouldtesting has a builtin fairness assumption. This is in itself a property long soughtafter; it is in notable contrast to the wellknown musttesting of De Nicola and Hennessy (denotationally characterised by a combination of failures and divergences), which treats divergence as catrastrophic and hence is incompatible with observation congruence. Due to these characteristics, shouldtesting supports modular reasoning and allows to use the proof techniques of observation congruence, but also supports additional laws and techniques.