is a semiautomaton,
a non-empty set of starting states, and
a set of final states or terminating states.
A triple is called a transition if , and is written . The set may contain more than one element (or none at all), which is why an automaton is also said to be non-deterministic. If on the other hand is a singleton for every , and is a singleton, then is said to be deterministic. In a deterministic automaton, can be viewed as a function from to .
If and are both finite, then is called a finite-state automaton, or FSA for short.
The state diagram of a finite-state automaton is constructed as if is being treated as a semiautomaton. In addition, a vertex corresponding to a starting state has an incoming arrow without a source, and a vertex corresponding to a final state has an outgoing arrow without a destination (alternatively, it may be represented by a double circle). This is illustrated in the following example:
Let be given by , where is the starting state, and the final state, , with the transition function given by the following table
|Date of creation||2013-03-22 12:26:34|
|Last modified on||2013-03-22 12:26:34|
|Last modified by||CWoo (3771)|