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The Power of Convex Algebras

Authors Filippo Bonchi, Alexandra Silva, Ana Sokolova

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Filippo Bonchi
Alexandra Silva
Ana Sokolova

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Filippo Bonchi, Alexandra Silva, and Ana Sokolova. The Power of Convex Algebras. In 28th International Conference on Concurrency Theory (CONCUR 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 85, pp. 23:1-23:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017) https://doi.org/10.4230/LIPIcs.CONCUR.2017.23

Abstract

Probabilistic automata (PA) combine probability and nondeterminism. 
They can be given different semantics, like strong bisimilarity, 
convex bisimilarity, or (more recently) distribution bisimilarity. 
The latter is based on the view of PA as transformers of probability 
distributions, also called belief states, and promotes distributions 
to first-class citizens.

We give a coalgebraic account of the latter semantics, and explain 
the genesis of the belief-state transformer from a PA. To do so, we 
make explicit the convex algebraic structure present in PA and 
identify belief-state transformers as transition systems with state 
space that carries a convex algebra. As a consequence of our abstract 
approach, we can give a sound proof technique which we call 
bisimulation up-to convex hull.

Subject Classification

Keywords
  • belief-state transformers
  • bisimulation up-to
  • coalgebra
  • convex algebra
  • convex powerset monad
  • probabilistic automata

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