Testing methods for X-machines: a review

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. Received June 2004 Revised March 2005 Accepted March 2005 by J. Derrick, M. Harman and R. M. Herons     

3-Col problem modelling using simple kernel P systems

This paper presents the newly introduced class of (simple) kernel P systems ((s)kP systems) and investigates through a 3-colouring problem case study the expressive power and efficiency of kernel P systems. It describes two skP systems that model the problem and analyses them in terms of efficiency and complexity. The skP models prove to be more succinct (in terms of number of rules, objects, number of cells and execution steps) than the corresponding tissue P system, available in the literature, that solves the same problem, at the expense of a greater length of the rules.     

Testing Conditions for Communicating Stream X-machine Systems

X-machines were proposed by Holcombe as a possible specification language and since then a number of further investigations have demonstrated that the model is intuitive and easy to use. In particular, stream X-machines (SXM), a particular class of X-machines, have been found to be extremely useful in practice. Furthermore, a method of testing systems specified as SXMs exists and is proved to detect all faults of the implementation provided that the system meets certain “design for test conditions”. Recently, a system of communicating SXMs was introduced as a means of modelling parallel processing. This paper proves that each communicating machine component can be transformed in a straightforward manner so that the entire system will behave like a single stream X-machine - the equivalent SXM of the system. The paper goes on to investigate the applicability of the SXM testing method to a system of communicating SXMs and identifies a class of communicating SXMs for which the equivalent SXM of the system meets the “design for test conditions”. Received November 1999 / Accepted in revised form June 2001     

A unified integration and component testing approach from deterministic stream X-machine specifications

One of the great benefits of using a stream X-machine to specify a system is its associated testing method. Under certain design for test conditions, this method produces a test suite that can determine the correctness of the implementation under test (IUT), provided that the basic components of the stream X-machine model have been correctly implemented. However, such an approach implies that each component can be tested in isolation from the rest of the system. This is a limitation that, in practice, can be resolved by developing stubs and drivers. However, this adds complexity to the testing process and, furthermore, these new pieces of software can introduce faults that can invalidate the theoretical results of the aforementioned testing method. This paper extends the approach by allowing component testing to be performed in parallel with integration testing, while still guaranteeing the IUT correctness under the given design for test conditions. It also shows how the integration test suite, produced in previous publications, can be reduced.