Formally, “*Finite automation is mathematical model of a system with discrete inputs and outputs”*. Finite automata describe a system or computer that goes through a fix number of states and has fixed inputs.

For people new to the topic, it is easier to understand using an example.

States and Symbol |

In this simple example, P and Q are states and ‘a’ is called input alphabet. From the figure we can see that there is transition from one state to another state on receiving the input ‘a’.

**Basic Definitions**

**Basic Definitions**

- A Finite automation (FA) consists of a finite
and a__set of states__from state to state that occur on a input symbols chosen from an alphabet ∑.**set of transitions** - For each input symbol there is exactly one
out to another state.**transition** **q0**is the. There is a state from which automation start all the transitions.**initial state**- Some states are
.**accepting states or Final states**

FA is denoted by 5-tuple ( Q, ∑, δ, q0, F ⊂) Q -> Finite number of States ( q0,q1,q2,q3). ∑ -> Finite number of symbols (a,b,c,d,e). δ -> Transition Function ( δ,a). q0 ->Initial State. F -> Final States (F⊆Q) where Q is finite number of states. |

**Example of Finite Automata**

**Example of Finite Automata**

Consider an finite automata that accepts even numbers binary equivalent.

meaning ,** 10** in binary is **1010.**

At q0 both 0 and 1 are even because they are 0, so q0 is accepting state. Now the automata must read the 1010 which is equal to Ten.

**Step 1: **

At First it received 1 and transition to q1

**Step 2:**

Then we received 0 and transition to q3

**Step 3:**

Then we received a 1 and transition to q2.

**Step 4:**

Finally, we received a 0, and goes to q0 with is an __ accepting state__.

Now, consider another example, automata reads

**1100**which is decimal

**12.**

**Step 1:**

First automata reads a 1, and automata goes to q1.

**Step 2:**

At q1, automata gets another 1 and goes back to q0 which is accepting state.

**Step 3:**

At q0, receives a 0 and goes to q2 state.

**Step 4:**

Finally, automata receives a 0 and goes to q0 final state.

**Transition Function **

**Transition Function**

A transition function is defined as** δ (q, a).**

Here **q** is some state and reads symbol **‘a’**, then enters **δ (q, a)** and moves to next state in automata.

If the next state is an accepting state** entire string** is accepted successfully.