Testing, betting and timed true concurrency

Abstract

The testing methodology is both appealingly simple and powerful as a way of analysing the behaviour of processes. In this paper we extend it in three ways.

Firstly we show how to incorporate the testing methodology into models where the notion of observation is central, rather than that of participation; we do this by introducing the notion of betting. This gives us a testing paradigm for true concurrency models such as event structures.

Secondly we introduce various timed bets to extend the methodology to timed models. An intuitively attractive semantics that admits a clear notion of rapidity of response is obtained.

Thirdly we show how bets can be extended to causal bets that allow us to reason about the causal behaviour of systems. The assumption that causality is observable is a strong one, but it may be justified if we read ‘concurrent’ as ‘physically distributed’.

Finally we classify the various betting semantics, presenting a hierarchy of semantics of increasing power. The semantics are presented with respect to a timed event structure model; they could, however, be applied to any (timed) causal model.