Composition and decomposition in true-concurrency

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. © Springer-Verlag Berlin Heidelberg 2005.