1. (extra credit points for the minimal correct solution. Submit your solution as a .jff file) The input to TM M is n1$n2, where n1 and n2 are strings of 1's and O's. If either n 1 or n2 starts with a 0, the output is n12n2; if n1 = n2, the output is n1=n2; when n1 and n2 are interpreted as the binary numbers m1 and m2 respectively, the output is n1<n2 if m1 < m2, and n1>n2 if m1 > m2. A correct implementation of M will have the transducer results below for the inputs in test cases.txt, included with the test materials. Input 1$1 10110$10110 1$10 1$11 10$11 101$110 10$1 11$1 101$100 1$01111 100$0 0001111$1 0$100 Output 1=1 10110=10110 1<10 1<11 10<11 101<110 10>1 11>1 101>100 1701111 100?0 0001111?1 0?100 Result Accept Accept Accept Accept Accept Accept Accept Accept Accept Accept Accept Accept Accept The file final.jff, also included with the test materials, encodes a partial implementation of M. It handles n1 = n2 correctly, as well as some, but not all, of the cases where m1 < m2, or m1 > m2. It does not handle cases where n1 or n2 starts with a 0. Enhance final.jff to implement M. To run the test cases in transducer mode, select Multiple Run (Transducer) from the Input menu, and then select Load Inputs from the buttons at the bottom of the right panel.

Fig: 1