The complexity of checking the existence and derivation of adaptive synchronizing experiments for deterministic FSMs

In this paper, we address the problem of setting a deterministic Finite State Machine (FSM) to a designated initial state. Differently from other papers, we propose to use adaptive synchronizing sequences (test cases) for this purpose and show that for weakly-connected deterministic complete reduced FSMs the problem of checking the existence of an adaptive synchronizing sequence is in P. For partial deterministic reduced FSMs the problem is PSPACE-complete.