A more precise implementation relation for distributed testing

There has been significant interest in distributed testing from an input output transition system. Previous work introduced an implementation relation $\dioco$ that was defined in terms of an equivalence relation on traces (sequences of observations). This paper considers an alternative approach in which an observation made in testing is a tuple of local traces, one for each tester. This paper defines such an implementation relation $\newdioco$ in terms of the possible observations regarding the system under test and the specification. It shows that $\newdioco$ is strictly weaker than $\dioco$ but is equivalent to $\dioco$ if processes cannot be output-divergent. Interestingly, this shows that the previous definition of $\dioco$ is too strong for output-divergent processes. We also prove that the Oracle problem is NP-complete but can be solved in polynomial time if there is an upper bound on the number of local testers