On the Equivalence of Controllability and the Input Output Conformance Testing Relation

Report, 2018

In this paper, the relation between controllability and the IOCO testing relationis examined. Based on a natural and common notion of controllability, where uncontrollableevents are interpreted as outputs from the plant, and viewing an implementation under testas a plant, the IOCO testing relation is equivalent to controllability. Further, it is shownhow supervisor synthesis can be used to algorithmically make an implementation IOCO withrespect to its specification. This can be done either by restricting the implementation to thesupremal controllable sublanguage, or extending the specification to the infimal controllablesuperlanguage, of the implementation and the specification. Both alternatives seem to be equallyviable, and the choice between them seem strongly application dependent.