Full-abstraction for client testing preorders.

•After a general introduction we recall the basic notion and existing results (Section 2).•In Section 3 we show an inductive characterisation of usable clients wrt must testing.•In Section 4 we give a coinductive characterisation of the Must client preorder.•Our characterisation us present the first decision procedure for this preorder.•After a brief digression about an expressiveness result, we characterise the compliance preorder for clients (Section 6).•Our results depend on auxiliary sets sharing order-theoretic justifications, suggesting a way to study testing preorders.