Algebraic laws of Regular Expression



Assume p, q, r are used in representing regular expressions, then the following algebraic laws holds true.

Union is Commutative    

p | q = q | r

Union is Associative

p | (q | r) = (p | q) | r

Concatenation is associative

p (qr) = (pq) r

Concatenation distributive over union

p (q | r) = pq | pr

(p | q) r = pr | qr

Identity for concatenation

εp = p ε = p

Closure

r*= (r | ε)*