Communicating Stream X-Machine (CSXM) The first fully formal model of concurrent X-machine composition was proposed in 1999 by Cristina Vertan and Horia Georgescu, based on earlier work on communicating automatata by Philip Bird and Anthony Cowling.<ref name="BC94">P. R. Bird and A. J. Cowling (1994) 'Modelling logic programming using a network of communicating machines', in Proc. 2nd Euromicro Workshop on Parallel and Distributed Processing, Malaga, 26–28 January 1994, pp. 156-161. Abstract</ref> In Vertan's model, the machines communicate indirectly, via a shared communication matrix (essentially an array of pigeonholes), rather than directly via shared channels. Bălănescu, Cowling, Georgescu, Vertan and others have studied the formal properties of this CSXM model in some detail. Full input/output relations can be shown. The communication matrix establishes a protocol for synchronous communication. The advantage of this is that it decouples each machine's processing from their communication, allowing the separate testing of each behaviour. This compositional model was proven equivalent to a standard Stream X-Machine, so leveraging the earlier testing theory developed by Holcombe and Ipate. This X-machine variant is discussed in more detail on a separate page. Object X-Machine (OXM) Kirill Bogdanov and Anthony Simons developed several variants of the X-machine to model the behaviour of objects in object-oriented systems. This model differs from the Stream X-Machine approach, in that the monolithic data type X is distributed over, and encapsulated by, several objects, which are serially composed; and systems are driven by method invocations and returns, rather than by inputs and outputs. Further work in this area concerned adapting the formal testing theory in the context of inheritance, which partitions the state-space of the superclass in extended subclass objects. A "CCS-augmented X-machine" (CCSXM) model was later developed by Simons and Stannett in 2002 to support complete behavioural testing of object-oriented systems, in the presence of asynchronous communication<ref name="SS02">M. Stannett and A. J. H. Simons (2002) 'CCS-Augmented X-Machines', Technical Report CS-2002-04, Department of Computer Science, Sheffield University, UK.</ref> This is expected to bear some similarity with NASA's recent proposal; but no definitive comparison of the two models has as yet been conducted. See also Stream X-Machine X-Machine Testing Communicating X-Machine Downloadable technical reports M. Stannett and A. J. H. Simons (2002) Complete Behavioural Testing of Object-Oriented Systems using CCS-Augmented X-Machines. Tech Report CS-02-06, Dept of Computer Science, University of Sheffield. Download J. Aguado and A. J. Cowling (2002) Foundations of the X-machine Theory for Testing. Tech Report