# Derivatives of Regular Expressions by Brzozowki Janusz.

What are the proofs for properties of Derivates of Regular Expressions (Brzozowski) using induction or equivalences?

These are two exercises about Derivatives of Regular Expressions by Brzozowki Janusz.

1. The first exercise is about proving using induction on regular expression r or equivalences that are in both articles attached (Owens and Brzozowski), the property of Derivative of Regular Expression r* (Kleene Star).
2. The second exercise is about defining an equation for derivative of regular expression r^+, that is similar to r* but epsilon (empty symbol) is not included. And prove it using induction on Regular Expression r or equivalences that are in both articles attached (Owens and Brzozowski).

By induction on r, there are these cases where Regular Expression r is:

– For Base Case :

1) empty

2) epsilon

3) symbol ‘a’ that belongs to Sigma (alphabet)

– For Induction Step:

1) a.b (concatenation)

2) a+b (union)

3) a* (Kleene Star)

Last Updated on September 23, 2018 by EssayPro