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An Algebra of Synchronous Atomic Steps

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FM 2016: Formal Methods (FM 2016)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9995))

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Abstract

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.

This work is supported by Australian Research Council (ARC) Discovery Project DP130102901 and the UK EPSRC Taming Concurrency research grant.

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Notes

  1. 1.

    We use the terms command, program and process synonymously.

  2. 2.

    Here our approach based on DRA differs from approaches based on Kleene algebra, like CKA and SKA, in which \(\top \) is also a right annihilator.

  3. 3.

    A semantic model for this interpretation may be found in [CHM16].

  4. 4.

    We use the syntax of Morgan’s specification command [q] [Mor88] whose definition is omitted for space reasons. It represents any sequence of atomic steps that establishes q between its initial and final states. See [CHM16] for details.

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Acknowledgements

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

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Authors and Affiliations

  1. School of Information Technology and Electrical Engineering, The University of Queensland, Brisbane, Australia

    Ian J. Hayes, Robert J. Colvin, Larissa A. Meinicke & Kirsten Winter

  2. School of Computing Science, Newcastle University, Newcastle upon Tyne, UK

    Andrius Velykis

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  1. Ian J. Hayes
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  2. Robert J. Colvin
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  3. Larissa A. Meinicke
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  4. Kirsten Winter
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  5. Andrius Velykis
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Correspondence to Ian J. Hayes .

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Editors and Affiliations

  1. Newcastle University, Newcastle upon Tyne, United Kingdom

    John Fitzgerald

  2. US Naval Research Laboratory, Washington, District of Columbia, USA

    Constance Heitmeyer

  3. ISTI-CNR, Pisa, Italy

    Stefania Gnesi

  4. University of Cyprus, Nicosia, Cyprus

    Anna Philippou

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Hayes, I.J., Colvin, R.J., Meinicke, L.A., Winter, K., Velykis, A. (2016). An Algebra of Synchronous Atomic Steps. In: Fitzgerald, J., Heitmeyer, C., Gnesi, S., Philippou, A. (eds) FM 2016: Formal Methods. FM 2016. Lecture Notes in Computer Science(), vol 9995. Springer, Cham. https://doi.org/10.1007/978-3-319-48989-6_22

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  • DOI: https://doi.org/10.1007/978-3-319-48989-6_22

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