Let AllButLast be a function that returns all of a string but its last character. For example, AllButLast(abc) = ab. AllButLast(λ) is undefined. Let R be any regular expression that does not generate λ. AllButLast(R) is the set of strings denoted by R, with AllButLast applied to each string. Thus AllButLast(a+b) a+. Show that AllButLast(R) is a regular set. Assume you now have a vocabulary consisting of the two letters, a and b.
Is Double a regular set? Why?