Bounded reordering in the distributed test architecture

In the distributed test architecture, the system under test interacts with its environment at multiple physically distributed ports and the local testers at these ports do not synchronise their actions. This presents many challenges and, in particular, apparently incorrect behaviours can be the consequence of an erroneous assumption about the exact order in which actions were performed at different ports. In previous work, we defined a conformance relation for the distributed test architecture. Essentially, the system under test is faulty if we observe a trace such that no admissible reordering of the actions in could have been produced by the specification. However, this notion can be weak if the compared traces might be too different. This paper introduces conformance relations where, for a given metric, a reordering is only considered if the distance between the two traces is at most a certain bound k. We introduce two different metrics and provide algorithms to construct finite automata accepting these close, with respect to each metric, sequences. We also study the computational complexity of the two main problems associated with the new framework: deciding whether a trace is accepted by the new automaton and deciding whether one system conforms to a specification with respect to the new conformance relation