Describing homing and distinguishing sequences for nondeterministic finite state machines via synchronizing automata

Abstract

There is a long standing problem of the study of homing and distinguishing sequences for deterministic and nondeterministic Finite State Machines (FSMs) which are widely used in many applications. A homing sequence allows establishing the state of the given FSM after applying the sequence while a distinguishing sequence allows learning the state of the given FSM before the sequence is applied. On the other hand, other sequences, namely, synchronizing sequences, have been thoroughly studied for finite automata. For a synchronizing automaton, there is a state such that a synchronizing sequence takes the automaton from any state to this state. There are many papers reported on such automata as well as on the complexity of synchronizing sequences. In this paper, given a complete nondeterministic FSM, we propose a method for deriving a corresponding finite automaton such that the set of all homing (or distinguishing) sequences coincides with the set of all synchronizing sequences of the derived automaton.