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Turing Machine Preliminaries
A Turing machine is specified by the following data
A finite set of symbols S = \$\{s_1,s_2,...\}\$
A finite set of states M = \$\{m_1,m_2,...\}\$
A partially defined function
$$T : M \times S \to S \times \{\mathrm{left},\mathrm{right}\} \times M $$
Any encoding ...