2025/01/31 by P. Wild, Wild, Paul, Lutz Schröder +1
Computer Science · #03B70 #68Q85 #Advanced Computational Techniques and Applications #Cognitive Computing and Networks #F.4.1 #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #Neural Networks and Applications
paper · pdf · doi:10.48550/arxiv.2502.00224
openalex publication_date 2025/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Behavioural conformances -- e.g. behavioural equivalences, distances, preorders -- on a wide range of system types (non-deterministic, probabilistic, weighted etc.) can be dealt with uniformly in the paradigm of universal coalgebra. One of the most commonly used constructions for defining behavioural distances on coalgebras arises as a generalization of the well-known Wasserstein metric. In this construction, couplings of probability distributions are replaced with couplings of more general objects, depending on the functor describing the system type. In many cases, however, the set of couplings of two functor elements is empty, which causes such elements to have infinite distance even in situations where this is not desirable. We propose an approach to defining behavioural distances and preorders based on a more liberal notion of coupling where the coupled elements are matched laxly rather than on-the-nose. We thereby substantially broaden the range of behavioural conformances expressible in terms of couplings, covering, e.g., refinement of modal transition systems and behavioural distance on metric labelled Markov chains.