On finite automata with quantum and classical states

Several quantum computational models were proposed in order to study how the quantum structure of matter could improve computational tasks. Among them, there are some that are based on finite automata, which are simpler computational devices, that helps to understand how a finite number of qubits could help to increase the power of the model. In this work, we study two-way finite automata with quantum and classical states (2QCFA), focusing on computability and complexity questions. We show results presented in the literature involving languages recognizability and closure properties and we then present some partial results on languages not recognized by the model.