Abstract: We extend the traditional nonnegative reward testing with negative rewards. In this new testing framework, may preorder and must preorder are the inverse of each other. More surprisingly, it turns out that the real reward must testing is no more powerful than the nonnegative reward testing, at least for finite processes. In order to prove that result, we exploit an important property of failure simulation about the inclusion of the testing outcomes between two related processes. © Shanghai Jiaotong University and Springer-Verlag Berlin Heidelberg 2011.

Key words: Failure simulation; Nonnegative reward testing; Probabilistic processes; Real reward testing