A Turing machine is an abstract model of an idealized computing device with unlimited time and storage space at its disposal. The device manipulates symbols, much as a human computing agent manipulates pencil marks on paper during arithmetical computation. Turing says very little about the nature of symbols. He assumes that primitive symbols are drawn from a finite alphabet. He also assumes that symbols can be inscribed or erased at “memory locations”. Turing’s model works as follows: