An Algebra of Synchronous Atomic Steps

  • Ian J. Hayes
  • Robert J. Colvin
  • Larissa A. Meinicke
  • Kirsten Winter
  • Andrius Velykis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9995)


This research started with an algebra for reasoning about rely/guarantee concurrency for a shared memory model. The approach taken led to a more abstract algebra of atomic steps, in which atomic steps synchronise (rather than interleave) when composed in parallel. The algebra of rely/guarantee concurrency then becomes an interpretation of the more abstract algebra. Many of the core properties needed for rely/guarantee reasoning can be shown to hold in the abstract algebra where their proofs are simpler and hence allow a higher degree of automation. Moreover, the realisation that the synchronisation mechanisms of standard process algebras, such as CSP and CCS/SCCS, can be interpreted in our abstract algebra gives evidence of its unifying power. The algebra has been encoded in Isabelle/HOL to provide a basis for tool support.


Boolean Algebra Parallel Operator Sequential Composition Parallel Composition Process Algebra 



This work has benefited from input from Cliff Jones and Kim Solin.


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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Ian J. Hayes
    • 1
  • Robert J. Colvin
    • 1
  • Larissa A. Meinicke
    • 1
  • Kirsten Winter
    • 1
  • Andrius Velykis
    • 2
  1. 1.School of Information Technology and Electrical EngineeringThe University of QueenslandBrisbaneAustralia
  2. 2.School of Computing ScienceNewcastle UniversityNewcastle upon TyneUK

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