L ? L = {uw | u ? L and w ? L}

DOUBLE(L) = {vv | v ? L}

STUTTER(L) = {w1w1w2w2 wnwn | n ? 0, wi ? ? for each i where 1 ? i ? n, and w1w2 wn ? L}

Note: ? is in each of these sets iff it is an element of L itself.

Consider the language E1 = {w ? {0, 1} ? | w ends in 1} = {u1 | u ? {0, 1} ?}. E1 is recognized by each of the machines below.

1. (10 points) In Individual HW0, we worked with the following operations: For L a set of strings, we can define the following associated sets DOUBLE(L)-(vu | u E L} STUTTER(L)-(wiw1WyWy . . . u'nu'n l n > 0. uIE ? for each i where 1 0. uIE ? for each i where 1