In this paper we consider a testing setting where the set of possible definitions of the Implementation Under Test (IUT), as well as the behavior of each of these definitions in all possible interactions, are extensionally defined, i.e., on an element-by-element and case-by-case basis. Under this setting, the problem of finding the minimum testing strategy such that collected observations will necessarily let us decide whether the IUT is correct or not (i.e., whether it necessarily belongs to the set of possible correct definitions or not) is studied in four possible problem variants: with or without non-determinism; and with or without more than one possible definition in the sets of possible correct and incorrect definitions. The computational complexity of these variants is studied, and properties such as PSPACE-completeness and Log-APX-hardness are identified.

翻译：本文研究一种测试场景，其中被测实现（IUT）的所有可能定义集合，以及每个定义在所有可能交互中的行为，都是外延定义的，即基于逐个元素和逐个案例的方式。在此场景下，我们研究了四种可能的问题变体中寻找最小测试策略的问题，使得收集到的观察结果必然能让我们判定IUT是否正确（即它是否必然属于可能正确定义的集合）：包含或不包含非确定性；以及在可能正确和错误定义的集合中是否允许多于一个可能的定义。本文研究了这些变体的计算复杂性，并识别出PSPACE完全性和Log-APX难解性等性质。