Question 3 (a) Construct a 2-tape DTM M that decides the language below (specify the TM in tabular compositional form) L, = {w E (0+1)* | w = u.u , u (0+1)*) (b) Repeat part (a) for Ly = {w E (0+1)* | w = u", u E (0+1)*) where N is a given integer constant Question 6 Construct in tabular compositional form the details of a 3-tape universal TM that uses the tape alphabet Ey ={#,0,1,$,';', (,)} with 7 characters, where tape 1 simulates the actual tape contents of the simulated DTM in encoded form ; tape 2 is read-only and has the contents of the transition function of the simulated TM in encoded form; and tape 3 has the contents of the encoded current state of the simulated TM ; all as described in class. To make life simple choose the encoding of the states and the input alphabet of the simulated machine in fixed number of binary digits by adding zeros to the left of the codes if necessary (else you will have expansion and compression problems in simulated tape contents). Question 3 (a) Construct a 2-tape DTM M that decides the language below (specify the TM in tabular compositional form) L, = {w E (0+1)* | w = u.u , u (0+1)*) (b) Repeat part (a) for Ly = {w E (0+1)* | w = u", u E (0+1)*) where N is a given integer constant Question 6 Construct in tabular compositional form the details of a 3-tape universal TM that uses the tape alphabet Ey ={#,0,1,$,';', (,)} with 7 characters, where tape 1 simulates the actual tape contents of the simulated DTM in encoded form ; tape 2 is read-only and has the contents of the transition function of the simulated TM in encoded form; and tape 3 has the contents of the encoded current state of the simulated TM ; all as described in class. To make life simple choose the encoding of the states and the input alphabet of the simulated machine in fixed number of binary digits by adding zeros to the left of the codes if necessary (else you will have expansion and compression problems in simulated tape contents)