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)* |