An algebraic theory of Markov processes

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Bacci, Giorgio and Mardare, Radu and Panangaden, Prakash and Plotkin, Gordon; (2018) An algebraic theory of Markov processes. In: LICS '18 : Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science. ACM, GBR, pp. 679-688. ISBN 9781450355834 (https://doi.org/10.1145/3209108.3209177)

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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.

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