
72 Computability Theory
3.3 Register Machines Over Words
1
The inputs to effective procedures are not really numbers, but numerals – strings of
symbols. For example, the input to a Turing machine consists of a string of symbols
written on consecutive squares of its tape. The register machines we have been con-
sidering up to now can be thought of as working with “base-1” numerals, where the
numeral for 7 is the string
|||||||
of seven tally marks. In base-1 notation, the increment and decrement commands are
the natural ones to use.
But suppose that we wanted our machines to work with binary numerals. In this
case, each register would contain some string ...