Lecture Notes in Computer Science 3472

coin
coin
e
c
coin
coin τ
5 Preorder Relations 141
coin
coffee
Fig. 5.12. Two vending machines (e ⊑R c; e �⊑FT c).
So we find that refusal preorder is coarser than observation preorder. This also
allows us to compare refusal and testing preorders. Indeed, recall that the infinite
processes shown in Figure 5.6 on page 133 are equivalent under observation
preorder (and then according to Proposition 5.12 under refusal preorder). We
have shown in the previous section that these processes are not equivalent under
testing preorder. Given that on the other hand refusal preorder distinguishes
between processes indistinguishable in testing preorder, we have
Corollary 5.13. The preorders ⊑T and ⊑R are not comparable.
We note here an apparent contradiction with results given elsewhere [Phi87]
that the two preorders are comparable. This contradiction turns out to be caused
by the unfortunate (and incorrect) terminology used in [Phi87].
In practical terms, refusal preorder is clearly more appealing than observation
preorder. Arguably, it is also more appealing than testing preorder, because of
the simplicity of tests; indeed, we eliminated all nondeterminism from the tests
in O1 and O2 (and thus in O). The only possible practical downside (of refusal
preorder compared with testing preorder) is that we need the ability to block
actions.
5.7 Failure Trace Testing
In refusal testing, whenever we observe a process that cannot continue because
we blocked all of its possible actions we have a failed test. This seems a reasonable
testing strategy, but we end up with surprising preorder relations because of it.
Consider for example the rather instructive example [Lan90] of the two vending
machines c and e depicted in Figure 5.12. Machine c may give us coffee if we