Abstract
In the study of behaviours of concurrent systems, traces are sets of behaviourally equivalent action sequences. Traces can be represented by causal partial orders. Step traces, on the other hand, are sets of behaviourally equivalent step sequences, each step being a set of simultaneous actions. Step traces can be represented by relational structures comprising non-simultaneity and weak causality. In this paper, we propose a classification of step alphabets as well as the corresponding step traces and relational structures representing them. We also explain how the original trace model fits into the overall framework.
Highlights
Mazurkiewicz traces [1,2] are a well-established, classical, and basic model for representing and structuring sequential observations of concurrent behaviour; see, e.g., [3]
The main aim of this paper is to investigate different classes of step traces obtained by restrictions on the simultaneity and sequentialisation relations, and to identify the corresponding relational structures
As the theorem shows, this result is optimal in the sense that for every relational structure in or ∈ ORsim\seq, there is a step trace defined by a step alphabet in sim\seq with the unlabelled order structure underlying or as its causal pattern
Summary
Mazurkiewicz traces [1,2] are a well-established, classical, and basic model for representing and structuring sequential observations of concurrent behaviour; see, e.g., [3]. The dependencies between the events of a trace are invariant among (common to) all elements of the trace They define an acyclic dependence graph which — through its transitive closure — determines the underlying causality structure of the trace as a (labelled) partial order [4]. There is a common acyclic dependence relation that underlies equivalent observations and is defined by the ordering of the occurrences of dependent actions, and its transitive closure interpreted as a causal partial order representing the trace to which wabu and wbau both belong.
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