Turing Machines and Computable Functions

Abstract

In earlier chapters we examined machines of steadily increasing power: pushdown automata were seen to be ‘stronger’ than finite-state automata, since any finite-state machine can be simulated by a pushdown machine, but not conversely. Similarly, linear bounded automata are ‘stronger’ than pushdown automata. If the definition of a linear bounded automaton is modified by removing the end-markers, so that the tape can increase in length without limit, a still more powerful class of machine is obtained. Machines of this type were first studied by Turing (1936), who introduced them in order to formalise the idea of an effective procedure, and since then they have been known as Turing machines.