**Transition In Automata**

Moving From one state to another or in same state with the help of arrow, by using an input alphabet is called **transition in Automata.** Transition happens with help of an input symbol and some rules.

**Notation of Transition**

Notation of transition is given below

**Example: **

DFA with ∑ = {0, 1} accepts all strings starting with 1.

**Solution:**

- In above finite automata transition graph, the machine initially is in initial state (q0) then on receiving input “b” the machine changes its state to q2.
- From q0 on receiving “a”, the machine changes its state to q1 from q0, which is the dead state.
- From q2 on receiving input “a”, “b” the machine changes its state to q2, which is the final state.
- The possible input strings that can be generated are ba, bb, bba, bab, bbb……., that means all string starts with “b”.
- In simple words, above machine can accept all strings which are starting with “b”.

**Transition Table**

Representation of the transition function in Tabular form is called transition table. Columns in Transition table are explained below

- First Column for all possible states.
- Rest all Columns for fix for each corresponding input symbols. It is also called next state after transition for specific corresponding input symbols.

**Note**: The initial state is denoted by an arrow with no source and final state is denoted by a star.

**Example **

**Solution:**

Transition table of above DFA is given below

Present State |
Next state for Input “a” |
Next State of Input “b” |

→q0 | q1 | q2 |

q1 | q0 | q2 |

*q2 | q2 | q2 |

**Explanation:**

- In the above transition table, the first column shows all the states and rest of the columns shows next state for each input.

**The first row of the transition table Shows**

- The current state is q0, on input ”a” the next state will be q1 and on input “b” the next state will be q2.

**The Second row of the transition table Shows**

- The current state is q1, on input “a”, the next state will be q0, and on input “b” the next state will be q2.

**The Third row of the transition table Shows**

- The current state is q2 on input “a”, the next state will be q2, and on “b” input the next state will be q2.