FOM: recursive definitions
Peter Manolios
pete at cs.utexas.edu
Fri Nov 2 22:13:42 EST 2001
I am interested in any references that relate to the following
question:
Under what conditions is a recursive equation satisfiable by some
total function?
Notice, that I am interested in total functions. If I were interested
in partial functions, then the first recursion theorem from recursive
function theory would be a good reference. However, that result is
not applicable here. To see why, consider the following recursive
equation.
f(x) = f(x)+1
The above is "monotone" as per the requirements of the first recusion
theorem, thus, there is a least partial function that satisfies the
equation, namely the nowhere defined function. However, there are no
total functions which satisfy the above equation.
Any references would be appreciated.
Pete Manolios
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