A Quick Review of Finite Automata

A Quick Review of Finite Automata

1. To make all this precise (and eventually prove that it works) we may need to refresh your knowledge of finite automata a bit.
2. First, recall the structure of a deterministic finite state machine.
   1. A finite set of states, .
   2. An input alphabet, .
   3. A transition function : x -> .
   4. A subset F of called the set of final states.
   5. An element ₀ of called the initial state.
3. While you are at it, recall (or at least note) that we can explain the behavior of a deterministic finite state machine by defining a function that extends to strings over the input alphabet. In particular, we can define : x ^* -> recursively as
   • ( , ) =
   • ( , x ) = ( ( , ), x )
   and then state that the language accepted by the machine is

   { ^*  | ( ₀, ) F }

A Quick Review of Finite Automata