Unrestricted stone duality for Markov processes

Furber, Robert and Kozen, Dexter and Larsen, Kim and Mardare, Radu and Panangaden, Prakash; (2017) Unrestricted stone duality for Markov processes. In: 2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS). IEEE, ISL, pp. 1-9. ISBN 9781509030194 (https://doi.org/10.1109/LICS.2017.8005152)

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Abstract

Stone duality relates logic, in the form of Boolean algebra, to spaces. Stone-type dualities abound in computer science and have been of great use in understanding the relationship between computational models and the languages used to reason about them. Recent work on probabilistic processes has established a Stone-type duality for a restricted class of Markov processes. The dual category was a new notion - Aumann algebras - which are Boolean algebras equipped with countable family of modalities indexed by rational probabilities. In this article we consider an alternative definition of Aumann algebra that leads to dual adjunction for Markov processes that is a duality for many measurable spaces occurring in practice. This extends a duality for measurable spaces due to Sikorski. In particular, we do not require that the probabilistic modalities preserve a distinguished base of clopen sets, nor that morphisms of Markov processes do so. The extra generality allows us to give a perspicuous definition of event bisimulation on Aumann algebras.

  • Item type:Book Section
    ID code:74748
    Dates:
    Date
    Event
    18 August 2017
    Published
    21 March 2017
    Accepted
    Notes:© 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
    Subjects:Science > Mathematics > Electronic computers. Computer science
    Department:Faculty of Science > Computer and Information Sciences
    Depositing user: Pure Administrator
    Date deposited:01 Dec 2020 14:45
    Last modified:11 Nov 2024 15:19
    URI:https://strathprints.strath.ac.uk/id/eprint/74748
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