A top-down approach is presented for checking the existence and derivation of an adaptive distinguishing test case (called also an adaptive distinguishing sequence) for a nondeterministic finite state machine (NDFSM). When such a test case exists, the method returns a canonical test case that includes all other distinguishing tests of the given complete observable NDFSM. In the second part of the paper, a constructive approach is provided for deriving a class of complete observable NDFSMs with n states, n > 2, and 2 n − n − 1 inputs such that a shortest adaptive distinguishing test case for each NDFSM in the intended class has the length (height) 2 n − n − 1. In other words, we prove the reachability of the exponential upper bound on the length of a shortest adaptive distinguishing sequence for complete observable NDFSMs while for deterministic machines the upper bound is polynomial with respect to the number of states. For constructing the intended class of NDFSMs for a given n , we propose a special linear order over all the non-empty subsets without singletons of an n -element set. The obtained tight exponential upper bound initiates further research on identifying certain NDFSM classes where this upper bound is not reachable.

中文翻译：

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非确定性有限状态机的自适应区分测试用例：测试用例推导和长度估计

提出了一种自上而下的方法来检查非确定性有限状态机（NDFSM）的自适应区分测试用例（也称为自适应区分序列）的存在和推导。当存在这样的测试用例时，该方法返回一个规范测试用例，其中包括给定完整可观察 NDFSM 的所有其他区别测试。在本文的第二部分，提供了一种构造方法来推导一类完整的可观察 NDFSM，其中n状态，n> 2 和 2 n -n− 1 个输入，使得目标类中每个 NDFSM 的最短自适应区分测试用例的长度（高度）为 2 n -n− 1. 换句话说，我们证明了完全可观察 NDFSM 的最短自适应区分序列长度的指数上限的可达性，而对于确定性机器，上限是关于状态数量的多项式。用于为给定的 NDFSM 构建预期的类n，我们对所有非空子集提出了一个特殊的线性顺序，没有单例n-元素集。获得的紧指数上限启动了进一步研究，以识别某些 NDFSM 类，其中该上限是不可达到的。