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On Three Alternative Characterizations of Combined Traces
The combined trace (i.e., comtrace) notion was introduced by Janicki and
Koutny in 1995 as a generalization of the Mazurkiewicz trace notion. Comtraces
are congruence classes of step sequences, where the congruence relation is
defined from two relations simultaneity and serializability on events. They
also showed that comtraces correspond to some class of labeled stratified order
structures, but left open the question of what class of labeled stratified
orders represents comtraces. In this work, we proposed a class of labeled
stratified order structures that captures exactly the comtrace notion. Our main
technical contributions are representation theorems showing that comtrace
quotient monoid, combined dependency graph (Kleijn and Koutny 2008) and our
labeled stratified order structure characterization are three different and yet
equivalent ways to represent comtraces. This paper is a revised and expanded
version of L\^e (in Proceedings of PETRI NETS 2010, LNCS 6128, pp. 104-124).Comment: 22 pages, preliminary versio