1. Simulate a TM with infinite tape on both ends using a two-track TM with finite storage

2. Prove the following language is non-Turing recognizable using the diagnolization principle { (M, w) | TM M, starts with input w, does not halt}

3. Construct a TM for L = {w| w contains equal number of 0's and 1's} over {0,1} a) provide an algorithmic description b) draw the transition diagram

4. Consider a language L = {0^m10ⁿ10^max(m,n)| m, n>= 0}. Construct a TM that decides the language. Describe the algorithm and draw the transition diagram of the TM.

5. Given the following TM M, does M a) accept or b) reject on inputs w1 = 000 and w2=0000? Show the content of the input tape and positions of the head step-by-step.