# What is a dead state in automata?

## What is a dead state in FA(DFA)?

We need to start a machine (DFA) to read a string. If machine reached successfully till its final string accepting state, then we say that string is accepted by our machine

But if we reach on a state where machine can’t move further to its final state, then this state is called dead state. Dead state is also known as dummy state.

## Example of dead state

In this example, machine will be start, then if we want to read strings that are starting with a then machine can reach to its final state to accept a string.

But if we start machine with b, then machine can’t move further to final state. After reading b we are moving to the dead state.

**Conclusion:**

Machine is at dead state, so string is not acceptable by machine.

**Note: **

- Dead state may be required in DFA.
- Dead state is not required in NFA.

## Why Dead state is not required in NFA?

Compare these two diagrams.

**DFA for regular expression of a(a+b)***

**NFA for regular expression of a(a+b)***

**Note:** DFA have only one transition of each alphabet from a state but NFA can have many transitions of one alphabet from a state. You can imagine that why dead state is not required in NFA because we have multiple ways to move to the final state.

## List of 100+ Important Deterministic Finite Automata

## Finite Automata Exercise Solution

Here I am showing you a list of some more important Deterministic Finite Automata used in the theory of automata and theory of computation.

- DFA for (a+b)* (a+b)a .
- DFA for (bb)*(aa)* .
- DFA for b+a(a+b)*+a.
- DFA for (a+b)*b+(bb)*a.
- DFA for bb+a(a+b)*+aa.
- DFA for a(a+b)*+bb(a)* .
- DFA for a(a+b)b*+bb(a)*.
- DFA for b(aa)*a+a(bb)*b.
- DFA for a+a(aa+b)*(aa)b.
- DFA for a+a(aa+b)*+(aa)b.
- DFA for (a+b)b(a+b)*+(aa)*b.
- FA for strings starting with a and ending with a.
- FA for the language of all those strings starting with a.
- FA for the language of all those strings containing aa as a substring.
- DFA for the language of all those strings starting and ending with the same letters.
- DFA for the language of all those strings starting and ending with different letters.
- DFA for the language of all those strings having double 0 or double 1.
- DFA for the language of all those strings starting and ending with b.
- DFA for ending with b.
- DFA for the string of even A’s and even b’s.
- DFA for the regular expression of a(a+b)*+(bb)+a(ba)*+aba+bb*(a+b)*.
- RegExp and DFA for strings having triple a’s or triple b’s.