Automata Theory - Final (Solutions)

1. Diagonalization: The Halting problem is defined as follows: Given a TuringMachineM = 〈Q, {0, 1},Γ, δ, q0,2, F 〉 and a string w ∈ Σ∗, determine whether M halts on w. In class, we proved that the Halting problem is undecidable using two different techniques. The first technique was constructive, where we constructed a series of Turing Machines, which led to a contradiction. The second technique was based on the observation that if the Halting problem is decidable then all recursively enumerable languages would become recursive. In this question, I am asking you to prove that the Halting problem is undecidable using diagonalization. Hint: Recall that the set of Turing Machines is countable and construct the table of Turing Machines presented with Turing Machines.