Turing Machine for i-Head Hydra

The Hydra was a many-headed monster in Greek mythology which terrorized visitors near the marsh/lake of Lerna in Greece. Killing the Hydra proved to be quite a challenge, as two heads would grow back whenever one was cut off. In this paper, we considered i-head Hydra given by Kirby and Paris. We have implemented i-head Hydra using a combination of Turing and Binary Turing machine. The developed Turing machine defines the ith hack in the hacking sequence. By using this Turing machine recursively, it is shown that the i-head hydra (finite) is doomed. Further the Hydra is related to the exponential growth of bacteria, which has been shown to be doomed with the help of the defined Turing Machine.