Enter the number of states, transitions, and final states into the calculator to determine Arden’s number. This calculator helps in the analysis of regular expressions and finite automata.

## Arden’s Theorem Formula

The following formula is used to calculate Arden’s number based on Arden’s Theorem.

A = m + (n - z)

Variables:

- A is Arden’s number
- n is the number of states in the finite automaton
- m is the number of transitions in the finite automaton
- z is the number of final states in the finite automaton

To calculate Arden’s number, add the number of transitions (m) to the difference between the number of states (n) and the number of final states (z).

## What is Arden’s Theorem?

Arden’s Theorem is a principle used in the field of computer science, specifically in the theory of computation and formal languages. It provides a method for constructing a regular expression that represents the language of a finite automaton. The theorem states that if P and Q are two regular expressions and P does not contain the empty string, then there is a unique regular expression R such that the language of R is the language of Q union the language of P followed by the language of R. Arden’s number is a concept derived from this theorem to help in the analysis of finite automata.

## How to Calculate Arden’s Number?

The following steps outline how to calculate Arden’s Number.

- First, determine the number of states (n) in the finite automaton.
- Next, determine the number of transitions (m) in the finite automaton.
- Next, determine the number of final states (z) in the finite automaton.
- Next, gather the formula from above = A = m + (n – z).
- Finally, calculate Arden’s Number (A).
- After inserting the variables and calculating the result, check your answer with the calculator above.

**Example Problem : **

Use the following variables as an example problem to test your knowledge.

Number of states (n) = 5

Number of transitions (m) = 8

Number of final states (z) = 2