Discrete-time recurrent neural networks (DTRNN) may be constructed using either threshold linear units (TLU) or units showing a continuous response such as sigmoid units. DTRNN using TLU were actually the earliest models of finite-state machines (FSM), as has been discussed in chapter 2, but in recent times there have been interesting theoretical advances in the representation of FSM in DTRNN; the corresponding papers are discussed in section 4.2.1. Sigmoid-based DTRNN have also recently been proven (by construction) to be able to behave as FSM; section 4.2.2 discusses the main issues involved and features three representative papers in the field.