Analysis of Reversible and Quantum Finite State Machines Using Homing, Synchronizing and Distinguishing Input Sequences

We present an analysis of the Reversible and Quantum Finite State Machines (QFSM) realized as Quantum Circuits using the three well known sequences applied in the analysis of the classical Finite State Machines (FSM). The synchronizing, the homing and the distinguishing sequences are applied to both strictly Reversible FSM (RFSM) and QFSM in order to determine the power of these new techniques in the above mentioned new models of sequential devices. In particular, care is taken to demonstrate these classical techniques on the RFSM and the one-way QFSMs. We show certain properties of the RFSM/QFSM with respect to these sequences and we show what are the restrictions and advantages.