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The X-machine testing method has been developed as an application of the W-method to testing the control structure of an implementation, against a specification. The method was proven to demonstrate the equivalence of the behaviour of the two, subject to a number of conditions both a specification and an implementation are expected to satisfy, such as (1) determinism of the two and (2) that functions labelling arcs on a transition diagram of a specification control structure have been tested in advance. Since the original publication of the testing method, a number of extensions have been published, removing the restrictions mentioned above. This paper surveys the extensions of the X-machine testing method, for (1) testing of functions together with testing of a transition diagram, (2) equivalence testing of a non-deterministic implementation against a non-deterministic specification, (3) conformance testing of a deterministic implementation against a non-deterministic specification and (4) equivalence testing of a system of concurrently executing and communicating X-machines, against a specification.

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