A behavioural pseudometric for probabilistic transition systems

• Published in: Theoretical computer science Vol. 331; no. 1; pp. 115 - 142
• Main Authors: van Breugel, Franck, Worrell, James
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Amsterdam Elsevier B.V 15.02.2005; Elsevier
• Subjects: Exact sciences and technology; General logic; General topics; Logic and foundations; Mathematical logic, foundations, set theory; Mathematics; Probabilistic bisimilarity; Probabilistic transition system; Probability and statistics; Probability theory and stochastic processes; Pseudometric; Real-valued modal logic; Sciences and techniques of general use; Terminal coalgebra; Probabilistic bisimilarity; Pseudometric; Real-valued modal logic; Probabilistic transition system; Terminal coalgebra; Computer theory; Semantics; Modal logic; Functor; Probability measure; Probability space
• ISSN: 0304-3975; 1879-2294
• DOI: 10.1016/j.tcs.2004.09.035

Discrete notions of behavioural equivalence sit uneasily with semantic models featuring quantitative data, like probabilistic transition systems. In this paper, we present a pseudometric on a class of probabilistic transition systems yielding a quantitative notion of behavioural equivalence. The pseudometric is defined via the terminal coalgebra of a functor based on a metric on the space of Borel probability measures on a metric space. States of a probabilistic transition system have distance 0 if and only if they are probabilistic bisimilar. We also characterize our distance function in terms of a real-valued modal logic.