Thread: Proof of (a*)* = a*

Hello,
can anybody help me to proove that (a*)* = a* in the algebra of regular expressions? The tutor says that we can exploit some similarity between regular expressions and regular sets.

Any idea?

Originally Posted by werken

Hello,
can anybody help me to proove that (a*)* = a* in the algebra of regular expressions? The tutor says that we can exploit some similarity between regular expressions and regular sets.

Any idea?

What does a* mean?

a is a regular expression denoting the regular set {a} for all items "a" that are members of the input alphabet sigma.

(nput alphabet sigma contains all terminal symbols that can be expected on input if it were an automaton.)

So basically "a" is any symbol from the input alphabet.