🤖 AI Summary
This study investigates the construction of minimal adaptive test strategies that are guaranteed to verify the correctness of an implementation under test (IUT) when its behavior is explicitly defined in an enumerated manner. Focusing on four problem variants arising from the interplay of nondeterminism and multiple definitions, the work employs formal modeling and reduction techniques to systematically analyze their computational complexity. It provides the first complete characterization of the complexity landscape for adaptive testing strategies within this extended model, establishing that several variants are PSPACE-complete or Log-APX-hard. These results lay a rigorous computational complexity foundation for the theory of adaptive testing.
📝 Abstract
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.