Editing X-machine (section)

=== Stream X-Machine (SXM) ===
{{main|Stream X-Machine}}
The most commonly encountered X-machine variant is Gilbert Laycock's 1993 ''[[Stream X-Machine]]'' (''[[SXM (computational model)|SXM]]'') model,<ref name="Lay" />
which forms the basis for Mike Holcombe and Florentin Ipate's theory of ''complete'' software testing, which guarantees known correctness properties, once testing is over.<ref name="HI98" /><ref name="IH98">F. Ipate and M. Holcombe (1998) 'A method for refining and testing generalised machine specifications'.
  ''Int. J. Comp. Math.'' '''68''', pp. 197-219.</ref>  The Stream X-Machine differs from Eilenberg's original model, in that the fundamental data type X is of the form ''Out''* × ''Mem'' × ''In''*, where ''In''* is an input sequence, ''Out''* is an output sequence, and ''Mem'' is the (rest of the) memory.

The advantage of this model is that it allows a system to be driven, one step at a time, through its states and transitions, while observing the outputs at each step.  These are witness values, that guarantee that particular functions were executed on each step.  As a result, complex software systems may be decomposed into a hierarchy of Stream X-Machines, designed in a top-down way and tested in a bottom-up way.  This divide-and-conquer approach to design and testing is backed by Florentin Ipate's proof of correct integration,<ref name="IpaHol97">F. Ipate and M. Holcombe (1997) 'An integration testing method that is proved to find all faults', ''International Journal of Computer Mathematics'' '''63''', pp. 159-178.</ref> which proves how testing the layered machines independently is equivalent to testing the composed system.