### Abstract

Original language | English |
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Title of host publication | Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2018 |

Number of pages | 10 |

Publisher | Association for Computing Machinery |

Publication date | 9 Jul 2018 |

Pages | 679-688 |

ISBN (Electronic) | 978-1-4503-5583-4 |

DOIs | |

Publication status | Published - 9 Jul 2018 |

Event | 33rd Annual ACM/IEEE Symposium on Logic in Computer Science - University of Oxford, Oxford, United Kingdom Duration: 9 Jul 2018 → 12 Jul 2018 http://lics.siglog.org/lics18/ |

### Conference

Conference | 33rd Annual ACM/IEEE Symposium on Logic in Computer Science |
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Location | University of Oxford |

Country | United Kingdom |

City | Oxford |

Period | 09/07/2018 → 12/07/2018 |

Internet address |

Series | Annual Symposium on Logic in Computer Science |
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ISSN | 1043-6871 |

### Fingerprint

### Keywords

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

### Cite this

*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

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*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.

Research output: Contribution to book/anthology/report/conference proceeding › Article in proceeding › Research › peer-review

TY - GEN

T1 - An Algebraic Theory of Markov Processes

AU - Bacci, Giorgio

AU - Mardare, Radu Iulian

AU - Panangaden, Prakash

AU - Plotkin, Gordon

PY - 2018/7/9

Y1 - 2018/7/9

N2 - 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.

AB - 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.

KW - Markov Processes

KW - Combining Monads

KW - Equational Logic

KW - Quantitative Reasoning

UR - http://www.scopus.com/inward/record.url?scp=85051119872&partnerID=8YFLogxK

U2 - 10.1145/3209108.3209177

DO - 10.1145/3209108.3209177

M3 - Article in proceeding

T3 - Annual Symposium on Logic in Computer Science

SP - 679

EP - 688

BT - Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2018

PB - Association for Computing Machinery

ER -