Optimal transfer trees and distinguishing trees for testing observable nondeterministic finite-state machines

The fault-state detection approach for blackbox testing consists of two phases. The first is to bring the system under test (SUT) from its initial state to a targeted state t and the second is to check various specified properties of the SUT at t. This paper investigates the first phase for testing systems specified as observable nondeterministic finite-state machines with probabilistic and weighted transitions. This phase involves two steps. The first step transfers the SUT to some state t´ and the second step identifies whether t´ is indeed the targeted state t or not. State transfer is achieved by moving the SUT along one of the paths of a transfer tree (TT) and state identification is realized by using diagnosis trees (DT). A theoretical foundation for the existence and characterization of TT and DT with minimum weighted height or minimum average weight is presented. Algorithms for their computation are proposed.