An Algebraic Theory of Markov Processes

Giorgio Bacci, Radu Iulian Mardare, Prakash Panangaden, Gordon Plotkin

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearchpeer-review

1 Citation (Scopus)

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 (Mardare et al LICS'16). We present the theory in a structured way using work of (Hyland et al. TCS'06) on combining monads. We take the interpolative barycentric algebras of (Mardare et al LICS'16) 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 publicationProceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2018
Number of pages10
PublisherAssociation for Computing Machinery
Publication date9 Jul 2018
Pages679-688
ISBN (Electronic)978-1-4503-5583-4
DOIs
Publication statusPublished - 9 Jul 2018
Event33rd Annual ACM/IEEE Symposium on Logic in Computer Science - University of Oxford, Oxford, United Kingdom
Duration: 9 Jul 201812 Jul 2018
http://lics.siglog.org/lics18/

Conference

Conference33rd Annual ACM/IEEE Symposium on Logic in Computer Science
LocationUniversity of Oxford
CountryUnited Kingdom
CityOxford
Period09/07/201812/07/2018
Internet address
SeriesAnnual Symposium on Logic in Computer Science
ISSN1043-6871

Fingerprint

Algebraic Theory
Markov Process
Axiomatization
Equational Logic
Centrobaric
Monads
Transition Systems
State Space
Metric
Algebra
Operator
Model

Keywords

  • Markov Processes
  • Combining Monads
  • Equational Logic
  • Quantitative Reasoning

Cite this

Bacci, G., Mardare, R. I., Panangaden, P., & Plotkin, G. (2018). An Algebraic Theory of Markov Processes. In Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2018 (pp. 679-688). Association for Computing Machinery. Annual Symposium on Logic in Computer Science https://doi.org/10.1145/3209108.3209177
Bacci, Giorgio ; Mardare, Radu Iulian ; Panangaden, Prakash ; Plotkin, Gordon. / An Algebraic Theory of Markov Processes. Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2018. Association for Computing Machinery, 2018. pp. 679-688 (Annual Symposium on Logic in Computer Science).
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Bacci, G, Mardare, RI, Panangaden, P & Plotkin, G 2018, An Algebraic Theory of Markov Processes. in Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2018. Association for Computing Machinery, Annual Symposium on Logic in Computer Science, pp. 679-688, 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, Oxford, United Kingdom, 09/07/2018. https://doi.org/10.1145/3209108.3209177

An Algebraic Theory of Markov Processes. / Bacci, Giorgio; Mardare, Radu Iulian; Panangaden, Prakash; Plotkin, Gordon.

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2018. Association for Computing Machinery, 2018. p. 679-688 (Annual Symposium on Logic in Computer Science).

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearchpeer-review

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Bacci G, Mardare RI, Panangaden P, Plotkin G. An Algebraic Theory of Markov Processes. In Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2018. Association for Computing Machinery. 2018. p. 679-688. (Annual Symposium on Logic in Computer Science). https://doi.org/10.1145/3209108.3209177