regex - Simplify this regular expression -

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i'm doing pre-exam exercises compilers class, , needed simplify regular expression.

(a u b)*(a u e)b* u (a u b)*(b u e)a*

quite obviously, e empty string, , u stands union.

so far, think 1 of (a u b)* can removed, union of u = a. however, can't find other simplifications, , not doing other problems far. :(

any appreciated, much!

little rusty on regex, if * still represents "zero or more ocurrences" can replace:

(a u e)b* (a u b)*

which leaves first part with:

(a u b)*(a u b)* = (a u b)*

on right side, have 

(b u e)a* = (b u a)*

now, since u b = b u a, get:

(a u b)*(a u b)*

on right hand side, leaves just

(a u b)* u (a u b)* = (a u b)*

i think that's it...


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