Testing methods for X-machines: a review

Abstract

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.

X-Machine Based Testing for Cloud Services

“…This property is not unusual for a cloud service, it is normal to expect a deterministic, repeatable behaviour, whenever the system is in the same configuration and receives the same input values. However, there exist also testing methodologies developed for nondeterministic X-machines [2] where the non-determinism can be caused either by overlapping functions domains or by non-determinism of the associated automaton A Z , i.e. F :…”

“…The testing methods for simple FSMs have been adapted to SXM testing [10,2,11,12], and consequently corresponding notions have been proposed to build the theoretical framework, such as realisable sequences, r-state cover, separating sets (which are sets of sequences of processing functions that differentiate between every pair of separable states of the machine [12]). …”

“…The first approach on testing using X-machines, the so called "DSXM integration testing" [15,13,10,2], was inspired by the W -method, and it can guarantee the conformance of the implementation, with respect to the SXM specification. The method was originally developed for testing the control structure of a system, modelled by a DSXM and it can be applied under some design for test conditions and the assumption that the processing functions of the X-machine have been correctly implemented (and previously tested).…”

Testing timed systems modeled by Stream X-machines

“…In further optimizations, this method has been modified to reduce the imposed conditions (e.g. [21,5,22]). As we have already explained, due to the fact that we remove most of the restrictions on machines, we cannot apply the previously mentioned methodologies to our extension of Stream X-machines.…”

Testing based on identifiable P Systems using cover automata and X-machines

“…This formalism elegantly and effectively combines the control aspects of the system with data structures, while allowing them to be separately described. Conformance testing for X-machines has been extensively studied and a number of test generation methods have been devised [2,19,13]. However, all these have been developed for a particular class of X-machines, called stream X-machines [14].…”