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. 1

bisimilarity

Abstract. History preserving (hp) and hereditary hp (hhp) bisimilarity are two equivalences for concurrent systems that reflect causal dependencies between events. hp bisimilarity is well-known to be decidable for finite-state systems, whereas the decidability of hhp bisimilarity had been a renowned open problem for several years until it was finally proved undecidable. Recently, the following positive result has been obtained: hhp bisimilarity coincides with hp bisimilarity for a class of live free choice systems. To our knowledge, this is the only positive result for a class with a reasonable amount of interplay between concurrency and of the proof that stands behind this result. The aim is to provide an overview of the modules involved and how they interact in the key results. We will not directly be concerned with hp and hhp bisimilarity in this paper, but with an auxiliary bisimilarity and its hereditary version. 1