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  Turing machines and the automata of equal power, Finite Automata with External Storage

Turing machines and the automata of equal power:

The Turing machine (TM, Alan Turing 1912-1954) is a FSM which controls a tape as an external storage device of the unbounded size. Access operations comprise read or write one symbol at a time, moving the read or write head one square at a time, and probably sensing the current end of the tape and extending it. The accurate form of access operations are not important, as long as they are adequately versatile to make the machine ‘universal’ in a sense that will be made accurate. This is amazing how little it takes to turn some of the restricted automata explained in this section to the TMS!

Creative exercise: The queue automaton (QA) or Post machine (Emil Post 1897-1954) or Tag machine is a FSM with single tape of unbounded length by FIFO access (that is, first-in first-out, as opposed to the LIFO access of the stack). M reads and deletes the symbol at the head of FIFO queue and might append a string to the tail end of queue. Technical detail: There is special symbol #, not part of alphabet A of the input string, in general used as a delimiter. Perhaps astonishingly, Post machines are universal, that is, equivalent in the computational power to TMs.

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