An Algebraic Theory of Markov Processes

Giorgio Bacci, Radu Mardare, Prakash Panangaden, Gordon Plotkin

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

Abstract

Markov processes are a fundamental model of probabilistic transition systems and are the underlying semantics of probabilistic programs. We give an algebraic axiomatisation of Markov processes using the framework of quantitative equational logic introduced in [13]. We present the theory in a structured way using work of Hyland et al. [9] on combining monads. We take the interpolative barycentric algebras of [13] which captures the Kantorovich metric and combine it with a theory of contractive operators to give the required axiomatisation of Markov processes both for discrete and continuous state spaces. This work apart from its intrinsic interest shows how one can extend the general notion of combining effects to the quantitative setting.
Original languageEnglish
Title of host publicationThirty-Third Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
Place of PublicationOxford, United Kingdom
PublisherACM
Pages679-688
Number of pages10
ISBN (Print)978-1-4503-5583-4
DOIs
Publication statusPublished - 9 Jul 2018
EventThirty-Third Annual ACM/IEEE Symposium on Logic in Computer Science - University of Oxford, Oxford, United Kingdom
Duration: 9 Jul 201812 Jul 2018
https://lics.siglog.org/lics18/

Conference

ConferenceThirty-Third Annual ACM/IEEE Symposium on Logic in Computer Science
Abbreviated titleLICS 2018
CountryUnited Kingdom
CityOxford
Period9/07/1812/07/18
Internet address

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