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In this paper we extend our previous work on passive testing of timed systems to establish a formal criterion to determine correctness of an implementation under test. In our framework, an invariant expresses the fact that if the implementation under test performs a given sequence of actions, then it must exhibit a behavior in a lapse of time reflected in the invariant. In a previous paper we gave an algorithm to establish the correctness of an invariant with respect to a specification. In this paper we continue the work by providing an algorithm to check the correctness of a log, recorded form the implementation under test, with respect to an invariant. We show the soundness of our method by relating it to an implementation relation. In addition to the theoretical framework we have developed a tool, called PASTE, that facilitates the automation of our passive testing approach.