State the relation among Regular Expression, Transition Diagram and Finite State Machines. By using a simple instance establish your claim.  

Answer: For each regular language, we can find out a FSM for this, because a FSM work as recognizer of a regular language. If a language is regular can be ascertained by finding whether a FSM can be drawn or not.  

A machine consists of finite number of states. To find out whether a string is valid or not, the FSM begins scanning the string from start state and moving together the transition diagram according to the current input symbol. The table displaying the movement from one state to other for input symbols of the alphabets is known as transition table.    

Each machine has a unique transition table. So, there is one to one relationship among Regular language and FSM and then between FSM and transition table.