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 diocoo in terms of the possible observations regarding the system under test and the specification. It shows that diocoo 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.