 Talk of “tape” and a “read-write head” is intended to aid the intuition (and reveals something of the time in which Turing was writing) but plays no important role in the definition of Turing machines. In situations where a formal analysis of Turing machines is required, it is appropriate to spell out the definition of the machinery and program in more mathematical terms. Purely formally a Turing machine can be specified as a quadruple \(T = (Q,\Sigma, s, \delta)\) where: