Acceptance of strings and Languages

The string and languages can be accepted by finite automata, when it reached to a finite state. There are two preferred notations for describing automata:
   Transition diagram;
A transition diagram or transition graph can be defined as collection of-

1.      Finite set of states Q

2.      Finite set of symbols∑.

3.      A non empty set S of Q. it is called start state.

4.      A set F subset of Q of final states

5.      A transition  function Q x A-> Q with as state and A as input from ∑^*.

The notations used in transition diagram are-

Example:

The FA can be represented a using transition graph. The machine initially is in start state q₀ then on receiving input 0 it changes to state q_1. From q_{1 \}receiving input 1the machine changes its state to q₄. The state q₄ is a final state or accept state. When we trace the input for transition diagram and reach to a final state at end of input string then it is said that the given input is accepted by transition diagram.

Transition Table:

This is a tabular representation of finite automata. For transition table the transition function is used.

Input state	0	1
q0	q1	q2
q1	-	q4
q2	q3	-
q3	q4	-
q4	-	-

The rows of the table correspond to states and columns of the table corresponding to inputs.