Your TM should implement the following pseudocode: Repeat until the head is over a 1: Cross off the 0 currently under the head Scan right past a 1 and any subsequent xs, and cross off the next 0 after the 1(reject if there is no 1, or no non-crossed-off 0 after the 1 but before the next 1) Continue scanning right past another 1 and any subsequent xs, then cross of the next 0 Scan left past both 1s and then until an x is reached, then back up one cell (Note: each non-rejecting iteration crosses off one 0 from each of the three groups) Scan right across the whole input, making sure there is a remaining 0 in the second group, and a remaining 0 in the third group, and no 1 after the third group (reject otherwise) Accept What is your tape alphabet? You may use the usual conventions for writing transitions, including omitting transitions that go to the reject state. 3. [20 points] Design a Turing machine (showing its state diagram) that decides the language {0i10j10k:i.