Logical Characterisations and Compositionality of Input-Output Conformance Simulation

Input-output conformance simulation (iocos) has been proposed by Gregorio-Rodr\'iguez, Llana and Mart\'inez-Torres as a simulation-based behavioural preorder underlying model-based testing. This relation is inspired by Tretman's classic ioco relation, but has better worst-case complexity than ioco and supports stepwise refinement. The goal of this paper is to develop the theory of iocos by studying logical characterisations of this relation and its compositionality. More specifically, this article presents characterisations of iocos in terms of modal logics and compares them with an existing logical characterisation for ioco proposed by Beohar and Mousavi. A precongruence rule format for iocos and a rule format ensuring that operations take quiescence properly into account are also given. Both rule formats are based on the GSOS format by Bloom, Istrail and Meyer.