2006 | OriginalPaper | Chapter
Invertible Classes
Authors : Sanjay Jain, Jochen Nessel, Frank Stephan
Published in: Theory and Applications of Models of Computation
Publisher: Springer Berlin Heidelberg
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This paper considers when one can invert general recursive operators which map a class of functions
$\mathcal{F}$
to
$\mathcal{F}$
. In this regard, we study four different notions of inversion. We additionally consider enumeration of operators which
cover
all general recursive operators which map
$\mathcal{F}$
to
$\mathcal{F}$
in the sense that for every general recursive operator Ψ mapping
$\mathcal{F}$
to
$\mathcal{F}$
, there is a general recursive operator in the enumerated sequence which behaves the same way as Ψ on
$\mathcal{F}$
. Three different possible types of enumeration are studied.