# Regular expression $(a^{*}b^{*})^{*} = \left( a+b \right)^{*}$ proof

Im having a lot of trouble proving that for the Regular expression $R_{1} = \left( a^{*} b^{*} \right)^{*}$ and $R_{2} = \left( a+b \right)^{*}$ that $L \left( R_{1} \right) = L \left( R_{2} \right)$. I was wondering if anyone could help me with this? thanks

• What specifically have you tried? What exactly is your trouble?
– Raphael
Oct 9, 2017 at 5:44
• what i tried to do is break it down as so: L((x+y)*) = L(x)* or L(y)* = {x}* or {y}* = {x,y}*, then for the L(xy)* = L(x*)*.L(y*)* = L(x*).L(y)* = {xy}*. But it ended up not working out.
– user78405
Oct 9, 2017 at 22:28
• "L((x+y)*) = L(x)* or L(y)* = {x}* or {y}* = {x,y}*" -- I don't know exactly what you mean here (logic needs parens, too!) but I can't read in a way that's correct. $(x+y)^*$ is not equivalent to $x^* + y^*$ (for all $x$, $y$).
– Raphael
Oct 10, 2017 at 7:27
• You can refer this answer, prove using Finite automata :stackoverflow.com/questions/8961632/… OR pages.cpsc.ucalgary.ca/~eberly/Courses/CPSC313/Syllabus/… for detailed proceudre and understanding Oct 12, 2017 at 5:29