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On Ethics of Mazurkiewicz Traces

Ochmański E., Pieckowska J.

Fundamenta Informaticae

2007

Vol. 80, nr 1-3

259-272

We extend the well-known hierarchy ∞-fair ⊆0-fair ⊆ just for sequences (sequential computations) to that of traces (concurrent processes). The fairness hierarchy for traces is similar, but more involved than for sequences. We study this hierarchy, first in general, abstracting from concrete concurrent system, then for basic classes of Petri nets - elementary and place/transition nets. Finally, we define the fairness notions in a non-interleaving way and compare them with the former ones.

Trace Nets and Conflict-free Computations

Ochmański E., Pieckowska J.

Fundamenta Informaticae

2006

Vol. 72, nr 1-3

311-321

Trace nets are a generalization of elementary nets, proposed by Badouel and Darondeau. They admit phenomena, unknown in traditional nets. For instance, in trace nets does not hold the "diamond property". For this reason, we propose a more precise definition of conflict, applicable to trace nets, and study occurrences of conflicts and existence of conflict-free runs in such nets. Main result of the paper says that any just computation in a trace net, starting from a conflict state, contains a conflict step. This result allows to construct an algorithm, selecting only conflict-free just computations from among all computations of a given net. All results of the paper hold for elementary nets, as they are a subclass of trace nets.