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A Complete Quantitative Deduction System for the Bisimilarity Distance on Markov Chains

Giorgio Bacci ; Giovanni Bacci ; Kim G. Larsen ; Radu Mardare.

In this paper we propose a complete axiomatization of the bisimilarity distance of Desharnais et al. for the class of finite labelled Markov chains. Our axiomatization is given in the style of a quantitative extension of equational logic recently proposed by Mardare, Panangaden, and Plotkin (LICS&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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Reasoning About Bounds in Weighted Transition Systems

Mikkel Hansen ; Kim Guldstrand Larsen ; Radu Mardare ; Mathias Ruggaard Pedersen.

We propose a way of reasoning about minimal and maximal values of the weights of transitions in a weighted transition system (WTS). This perspective induces a notion of bisimulation that is coarser than the classic bisimulation: it relates states that exhibit transitions to bisimulation classes with&nbsp;[&hellip;]

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