For Finite State Machines (FSMs) a rich testing theory has been developed to discover aspects of their behavior and ensure their correct functioning. Although this theory has been frequently used, e.g. to check conformance of protocol implementations, its applicability is limited by restrictions of FSMs, in which inputs and outputs alternate, and outputs are determined by the previous input and state. Labeled Transition Systems with inputs and outputs (LTSs), as studied in ioco testing theory, provide a richer framework for testing component oriented systems, but lack the algorithms for test generation from FSM theory.

In this article, we propose an algorithm for the fundamental problem of state identification during testing of LTSs. Our algorithm is a direct generalization of the well-known algorithm for computing adaptive distinguishing sequences for FSMs proposed by Lee and Yannakakis. Our algorithm has to deal with so-called compatible states, states that cannot be distinguished. Analogous to the result of Lee and Yannakakis, we prove that if an adaptive test exists that distinguishes all pairs of (incompatible) states of an LTS, our algorithm will find one. In practice, such perfect adaptive tests typically do not exist. However, in experiments with an implementation of our algorithm on a collection of (both academic and industrial) benchmarks, we find that that the adaptive tests produced by our algorithm still distinguish at least 99% of the incompatible state pairs.

对于有限状态机 (FSM)，已经开发出丰富的测试理论来发现其行为的各个方面并确保其正确运行。虽然这个理论经常被使用，例如检查协议实现的一致性，但它的适用性受到 FSM 的限制，其中输入和输出交替，输出由先前的输入和状态决定。ioco 测试理论中研究的具有输入和输出的标记转换系统 (LTS)，为测试面向组件的系统提供了更丰富的框架，但缺乏 FSM 理论中用于测试生成的算法。

在本文中，我们针对LTS 测试期间状态识别的基本问题提出了一种算法。我们的算法是著名算法的直接推广，用于计算 Lee 和 Yannakakis 提出的 FSM 自适应区分序列。我们的算法必须处理所谓的兼容状态，无法区分的状态。类似于 Lee 和 Yannakakis 的结果，我们证明如果存在一个自适应测试来区分 LTS 的所有（不兼容）状态对，我们的算法将找到一个。在实践中，这种完美的自适应测试通常不存在。然而，在我们的算法在一系列（学术和工业）基准上的实现实验中，我们发现我们的算法产生的自适应测试仍然区分了至少 99% 的不兼容状态对。