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Approximate reasoning for real-time probabilistic processes

Vineet Gupta ; Radha Jagadeesan ; Prakash Panangaden.

We develop a pseudo-metric analogue of bisimulation for generalized semi-Markov processes. The kernel of this pseudo-metric corresponds to bisimulation; thus we have extended bisimulation for continuous-time probabilistic processes to a much broader class of distributions than exponential&nbsp;[&hellip;]

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Free complete Wasserstein algebras

Radu Mardare ; Prakash Panangaden ; Gordon D. Plotkin.

We present an algebraic account of the Wasserstein distances $W_p$ on complete metric spaces, for $p \geq 1$. This is part of a program of a quantitative algebraic theory of effects in programming languages. In particular, we give axioms, parametric in $p$, for algebras over metric spaces equipped&nbsp;[&hellip;]

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A categorical characterization of relative entropy on standard Borel spaces

Nicolas Gagne ; Prakash Panangaden.

We give a categorical treatment, in the spirit of Baez and Fritz, of relative entropy for probability distributions defined on standard Borel spaces. We define a category suitable for reasoning about statistical inference on standard Borel spaces. We define relative entropy as a functor into&nbsp;[&hellip;]

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Sum and Tensor of Quantitative Effects

Giorgio Bacci ; Radu Mardare ; Prakash Panangaden ; Gordon Plotkin.

Inspired by the seminal work of Hyland, Plotkin, and Power on the combination of algebraic computational effects via sum and tensor, we develop an analogous theory for the combination of quantitative algebraic effects. Quantitative algebraic effects are monadic computational effects on categories of&nbsp;[&hellip;]

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