  Various relations have been defined to express refinement and conformance for
state-transition systems with inputs and outputs, such as ioco and uioco in the
area of model-based testing, and alternating simulation and alternating-trace
containment originating from game theory and formal verification. Several
papers have compared these independently developed relations, but these
comparisons make assumptions (e.g., input-enabledness), pose restrictions
(e.g., determinism - then they all coincide), use different models (e.g.,
interface automata and Kripke structures), or do not deal with the concept of
quiescence. In this paper, we present the integration of the ioco/uioco theory
of model-based testing and the theory of alternating refinements, within the
domain of non-deterministic, non-input-enabled interface automata. A standing
conjecture is that ioco and alternating-trace containment coincide. Our main
result is that this conjecture does not hold, but that uioco coincides with a
variant of alternating-trace containment, for image finite interface automata
and with explicit treatment of quiescence. From the comparison between ioco
theory and alternating refinements, we conclude that ioco and the original
relation of alternating-trace containment are too strong for realistic
black-box scenarios. We present a refinement relation which can express both
uioco and refinement in game theory, while being simpler and having a clearer
observational interpretation.
