Invertible Classes

  • Sanjay Jain
  • Jochen Nessel
  • Frank Stephan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3959)


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.


Recursive Function Inductive Inference Total Function Recursive Operator Acceptable Numbering 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Sanjay Jain
    • 1
  • Jochen Nessel
    • 2
  • Frank Stephan
    • 3
  1. 1.School of ComputingNational University of SingaporeRepublic of Singapore
  2. 2.College of Business Administration for ManagersHo Chi Minh CityVietnam
  3. 3.Department of MathematicsNational University of SingaporeRepublic of Singapore

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