Abstract
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.
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Jain, S., Nessel, J., Stephan, F. (2006). Invertible Classes. In: Cai, JY., Cooper, S.B., Li, A. (eds) Theory and Applications of Models of Computation. TAMC 2006. Lecture Notes in Computer Science, vol 3959. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11750321_67
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DOI: https://doi.org/10.1007/11750321_67
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34021-8
Online ISBN: 978-3-540-34022-5
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