Vaandrager compares different notions of equivalence between deterministic event structures. The event structures are endowed with a causal relation that is a partial ordering; consequently, each event may be regarded as a prerequisite (and a successor) of itself, and no nontrivial event loops are possible. This greatly reduces the applicability of the results. It is also important to realize, as the author goes to great lengths to explain, that the notion of determinism used in the paper is not universal. For those readers who are more interested in the application of the results than in their formal derivation, this point is crucial. The author’s stance is that an event structure is deterministic if from each configuration, a given event causes a move to a unique next configuration. The paper does not consider structures in which a configuration may have two or more conflicting events enabled and there is a free choice of which is performed. The author argues that his definition is appropriate for modeling “reactive systems,” but even for such systems external stimuli are sometimes in conflict.

With these definitions, the author formulates different equivalence relations over his event structures--isomorphism, bisimulation, sequence equivalence, step sequence equivalence, pomset (partially ordered multiset) equivalence, and split sequence equivalence. He demonstrates their interrelationships and, in the deterministic case, shows that several of them coincide. The definition of an event structure includes an event labeling function about which little is said. This omission is a pity, since labelings rather than the actual events are often used in the figures.

The paper concludes with a discussion of how, for deterministic systems, concurrent actions may be split so that the causal structure can be deduced by an observer who can detect the start and finish of each event. Although the mathematics is presented in a slightly contracted form, the proofs are easy to follow, and the results are well cross-referenced to earlier work by others. This paper makes a useful but narrow contribution to the literature.