Finite Automata

Overview


Intuition


A finite automata is a machine that takes a sequence of inputs, processes those inputs in turn, and returns an answer of some sort.

Definition


A Finite Automata is described by the following elements

  • A set of states, label {% Q %}
  • A set of symbols, representing the alphabet used by the machine, labeled {% \Sigma %}
  • A function, {% \delta : Q \times \Sigma \rightarrow Q %}, which determines what the machine does. It takes the current state of the machine, and the next input, and returns the next state of the machine.
  • An element {% q_0 \in Q %} that represents the state the machine starts in