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IFIP WG1.3 Foundations of System Specification

Talk "The Power of (Convex) Algebras"

by Ana Sokolova

Mon, 09 January 2017 at 05:00 pm in Binz (Rügen), Germany

Joint work with: Filippo Bonchi and Alexandra Silva

Abstract: In several papers in the last several years, the semantics of probabilistic automata is expressed via transformers of belief states, which are probability distributions over original states. In this work, we provide the necessary abstract theory to explain the involved transformations. We unravel the true nature of probabilistic automata as coalgebras over (convex) algebras. Convex algebras are the Eilenberg-Moore algebras of the distribution monad. We construct suitable functors over the category EM(D) of Eilenberg-Moore algebras of the distribution monad, among which a convex-powerset functor (monad), the constant exponent functor, and two ways of a lift functor (monad).