Unrestricted stone duality for Markov processes

Robert Furber, Dexter Kozen, Kim Guldstrand Larsen, Radu Iulian Mardare, Prakash Panangaden

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4 Citationer (Scopus)

Abstrakt

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.
OriginalsprogEngelsk
Titel2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
ForlagIEEE Press
Publikationsdato8 aug. 2017
Artikelnummer8005152
ISBN (Trykt)978-1-5090-3019-4
ISBN (Elektronisk)9781509030187
DOI
StatusUdgivet - 8 aug. 2017
Begivenhed2017 32nd Annual ACM/
IEEE Symposium on Logic in Computer Science (LICS)
- Reykjavík University in Iceland, Reykjavík , Island
Varighed: 20 jun. 201723 jun. 2017
https://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=7999337

Konference

Konference2017 32nd Annual ACM/
IEEE Symposium on Logic in Computer Science (LICS)
LokationReykjavík University in Iceland
LandIsland
ByReykjavík
Periode20/06/201723/06/2017
Internetadresse

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