Composition and decomposition in true-concurrency

  • Authors:
  • Sibylle Fröschle

  • Affiliations:
  • Institute of Informatics, University of Warsaw, Poland

  • Venue:
  • FOSSACS'05 Proceedings of the 8th international conference on Foundations of Software Science and Computation Structures
  • Year:
  • 2005

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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.