Re: Question on language regularity

Eric Bodden wrote:
"Let L be a regular language. Is the following language regular?
R_L := {a_2 a_1 a_4 a_3 ... a_(2n) a_(2n-1) | a1 a2 a3 ... a_(2n) in
L}"
[...]
Does anybody have any idea how to approach this?

Can you come up with a regular transducer (a Mealy/Moore machine)
that produces a_2 a_1 a_4 a_3 ... a_(2n) a_(2n-1) as its output when
given a1 a2 a3 ... a_(2n) as its input?
.