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Generalizing Simulation to Abstract Domains

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Book cover CONCUR 2013 – Concurrency Theory (CONCUR 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8052))

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Abstract

We introduce a notion of subsumption for domains used in abstract interpretation. We show that subsumption has the same properties and applications in the context of abstract interpretation that simulation has for transition systems. These include a modal characterisation theorem, a fixed point characterisation, and the construction of property-preserving abstractions. We use the notion of conjugate functions from algebraic logic to develop bisubsumption, an order-theoretic generalisation of bisimulation to Boolean domains. We prove a representation theorem that relates simulation and subsumption.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of California, Berkeley, USA

    Vijay D’Silva

Authors
  1. Vijay D’Silva
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Editors and Affiliations

  1. Facultad de Matemáticas, Astronomía y Física, Universidad Nacional de Córdoba – CONICET, Medina Allende s/n,, X5000HUA, Córdoba, Argentina

    Pedro R. D’Argenio

  2. Departamento de Computación,, Universidad de Buenos Aires - Conicet, Intendente Güirales 2160, C1428EGA, Ciudad Autónoma de Buenos Aires, Argentina

    Hernán Melgratti

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D’Silva, V. (2013). Generalizing Simulation to Abstract Domains. In: D’Argenio, P.R., Melgratti, H. (eds) CONCUR 2013 – Concurrency Theory. CONCUR 2013. Lecture Notes in Computer Science, vol 8052. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40184-8_34

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  • DOI: https://doi.org/10.1007/978-3-642-40184-8_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40183-1

  • Online ISBN: 978-3-642-40184-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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