Deriving adaptive homing sequences for weakly initialized nondeterministic FSMs

Abstract

State identification sequences, such as homing and distinguishing sequences (HS and DS), are widely used in FSM (Finite State Machine) based testing in order to reduce the size of a returned complete test suite as well as minimize checking efforts in passive testing. Preset HS are known to always exist for deterministic complete reduced FSMs but it is not the case for nondeterministic FSMs. It is also known that in this case, adaptive HS exist more often and usually are shorter than the preset. Nowadays, a number of specifications are represented by nondeterministic FSMs and thus, a deeper study of such sequences is required. There exist sufficient and necessary conditions for the existence of an adaptive HS for complete nondeterministic FSMs when each state can be an initial state but those conditions become only sufficient for weakly initialized FSMs where only some states are initial. In this paper, we propose sufficient and necessary conditions for a weakly initialized FSM to have an adaptive homing sequence, possibly up to given length, which are based on deriving an appropriate so-called homing FSM. The experimental evaluation of the existence of adaptive and preset HS is performed for randomly generated FSMs.