Unrestricted stone duality for Markov processes

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

1 Citation (Scopus)

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.

Original languageEnglish
Title of host publication32nd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2017
Number of pages9
ISBN (Electronic)9781509030187
DOIs
Publication statusPublished - 8 Aug 2017
Event32nd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2017 - Reykjavik, Iceland
Duration: 20 Jun 201723 Jun 2017

Conference

Conference32nd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2017
CountryIceland
CityReykjavik
Period20/06/1723/06/17

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Keywords

  • Markov processes
  • extraterrestrial measurements
  • boolean algebra
  • probabilistic logics
  • computational modeling
  • topology
  • duality (mathematics)
  • set theory

Cite this

Furber, R., Kozen, D., Larsen, K., Mardare, R., & Panangaden, P. (2017). Unrestricted stone duality for Markov processes. In 32nd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2017 [8005152] https://doi.org/10.1109/LICS.2017.8005152