Studying the separability relation between finite state machines

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Abstract

Several authors have studied the relationships between non-deterministic finite state machines (FSMs). These relationships can be used, for example, for deriving conformance tests from specifications represented by FSMs. In this paper, the separability relation between FSMs is studied. In particular, an algorithm is presented that derives a shortest separating sequence of two non-deterministic FSMs. Given FSMs S with n states and T with m states, it is shown that the upper bound on the length of a shortest separating sequence is 2mn−1. Moreover, the upper bound is shown to be reachable. However, according to the conducted experiments, on average, the length of a shortest separating sequence of FSMs S and T states is less than mn and the existence of a separating sequence significantly depends on the number of non-deterministic transitions in these FSMs. The proposed algorithm can also be used for deriving a separating sequence of two different states of a single FSM or for deriving a separating sequence of three or more FSMs. Copyright © 2007 John Wiley & Sons, Ltd.

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