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Composition and Decomposition in True-Concurrency.

Fröschle, Sibylle

In: Vladimiro Sassone (Ed.): Lecture Notes in Computer Science, Vol. 3441: Foundations of Software Science and Computational Structures: 8th International Conference, FOSSACS 2005, Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2005, Edinburgh, UK, April 4-8, 2005, pages 333-347. Springer-Verlag, 2005.

Abstract: The idea of composition and decomposition to obtain computability results is particularly relevant for true-concurrency. In contrast to the interleaving world, where composition and decomposition must be considered with respect to a process algebra operator, e.g. parallel composition, we can directly recognize whether a truly-concurrent model such as a labelled asynchronous transition system or a 1-safe Petri net can be dissected into independent chunks of behaviour. In this paper we introduce the corresponding concept decomposition into independent components, and investigate how it translates into truly-concurrent bisimulation equivalences. We prove that, under a natural restriction, history preserving (hp), hereditary hp (hhp), and coherent hhp (chhp) bisimilarity are decomposable with respect to prime decompositions. Apart from giving a general proof technique our decomposition theory leads to several coincidence results. In particular, we resolve that hp, hhp, and chhp bisimilarity coincide for normal form basic parallel processes.

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