A behavioural pseudometric for metric labelled transition systems

Abstract

Metric labelled transition systems are labelled transition systems whose states and actions form (pseudo)metric spaces. These systems can capture a large class of timed transition systems, including systems with uncountably many states and uncountable nondeterminism. In this paper a behavioural pseudometric is introduced for metric labelled transition systems. The behavioural distance between states, a nonnegative real number, captures the similarity of the behaviour of those states. The smaller the distance, the more alike the states are. In particular, the distance between states is 0 iff they are bisimilar. Three different characterisations of this pseudometric are given: a fixed point, a logical and a coinductive characterisation. These generalise the fixed point, logical and coinductive characterisations of bisimilarity. © Springer-Verlag Berlin Heidelberg 2005.