  Homing preset and adaptive experiments with Finite State Machines (FSMs) are
widely used when a non-initialized discrete event system is given for testing
and thus, has to be set to the known state at the first step. The length of a
shortest homing sequence is known to be exponential with respect to the number
of states for a complete observable nondeterministic FSM while the problem of
checking the existence of such sequence (Homing problem) is PSPACE-complete. In
order to decrease the complexity of related problems, one can consider adaptive
experiments when a next input to be applied to a system under experiment
depends on the output responses to the previous inputs. In this paper, we study
the problem of the existence of an adaptive homing experiment for complete
observable nondeterministic machines. We show that if such experiment exists
then it can be constructed with the use of a polynomial-time algorithm with
respect to the number of FSM states.
