Finite State Machine is a model to describe how the internal state of the machine varies due to the corresponding actions. The number of states of the machine are limited as the name suggests.

no

I would guess that is because it has a finite number of different states. (It is also known as a finite-state machine.)

NFA - Non-deterministic Finite Automaton, aka NFSM (Non-deterministic Finite State Machine)

http://www.tcpipguide.com/free/t_DHCPGeneralOperationandClientFiniteStateMachine.htm